Problem:
Score : 500 points

Problem Statement

Given are N positive integers A_1,...,A_N.

Consider positive integers B_1, ..., B_N that satisfy the following condition.

Condition: For any i, j such that 1 \leq i < j \leq N, A_i B_i = A_j B_j holds.

Find the minimum possible value of B_1 + ... + B_N for such B_1,...,B_N.

Since the answer can be enormous, print the sum modulo (10^9 +7).

Constraints

1 \leq N \leq 10^4

1 \leq A_i \leq 10^6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 ... A_N

Output

Print the minimum possible value of B_1 + ... + B_N for B_1,...,B_N that satisfy the condition, modulo (10^9 +7).

Sample Input 1

3
2 3 4

Sample Output 1

13

Let B_1=6, B_2=4, and B_3=3, and the condition will be satisfied.

Sample Input 2

5
12 12 12 12 12

Sample Output 2

5

We can let all B_i be 1.

Sample Input 3

3
1000000 999999 999998

Sample Output 3

996989508

Print the sum modulo (10^9+7).

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;

public class Main {
	static int[] arr;
	static int N;
	static int commonGcd;
	static List<HashMap<Integer, Integer>> pplist = new ArrayList<HashMap<Integer, Integer>>();
	static int PN = 1000000;
	static List<Integer> prime = new ArrayList<Integer>();
	static Map<Integer, Boolean> primeMap = new HashMap<Integer, Boolean>();

	public static void main(String[] args) throws NumberFormatException, IOException {
		init();
		read();
		ppList();
	}

	private static void ppList() {
		HashMap<Integer, Integer> maxMap = new HashMap<Integer, Integer>();
		for (int i = 0; i < N; i++) {
			int A = arr[i] / commonGcd;
			compute(maxMap, A);
		}

		long sum = 0;
		for (int i = 0; i < N; i++) {
			HashMap<Integer, Integer> map = pplist.get(i);
			long t = 1;
			for (Integer p : maxMap.keySet()) {
				int count = maxMap.get(p);
				int count2 = (map.get(p) == null ? 0 : map.get(p));

				t = t * pow(p, count - count2) % 1000000007;
			}
			sum = (sum + t) % 1000000007;
		}
		System.out.println(sum);
	}

	private static long pow(int a, int p) {
		if (p == 1) {
			return a;
		}
		if (p == 0) {
			return 1;
		}
		int res = 1;
		int p2 = a * a;
		for (int t = 2; t <= p; t += 2) {
			res = res * p2;
		}
		res = res * (p % 2 == 1 ? a : 1);
		return res;
	}

	private static void compute(HashMap<Integer, Integer> maxMap, int A) {
		HashMap<Integer, Integer> tmpMap = new HashMap<Integer, Integer>();
		for (int i = 0, size =prime.size(); i < size;) {

			if (primeMap.get(A) != null) {

				Integer count = tmpMap.get(A);

				if (count == null) {
					tmpMap.put(A, 1);
				} else {
					tmpMap.put(A, count + 1);
				}

				break;
			}

			else if (A % prime.get(i) == 0) {
				int p =  prime.get(i);

				Integer count = tmpMap.get(p);

				if (count == null) {
					tmpMap.put(p, 1);
				} else {
					tmpMap.put(p, count + 1);
				}

				A = A / p;
			} else {
				i++;
			}
		}

		for (Entry<Integer, Integer> entry : tmpMap.entrySet()) {
			int p = entry.getKey();
			int count = entry.getValue();

			Integer currCount = maxMap.get(p);

			if (currCount == null || currCount <= count) {
				maxMap.put(p, count);
			}
		}
		pplist.add(tmpMap);

	}

	private static int gcd(int a, int b) {
		if (b % a == 0) {
			return a;
		} else {
			return gcd(b % a, a);
		}
	}

	private static void read() throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		N = Integer.parseInt(br.readLine());
		String[] wrods = br.readLine().split(" ");
		arr = new int[wrods.length];
		for (int i = 1; i <= N; i++) {
			arr[i - 1] = Integer.parseInt(wrods[i - 1]);
			if (i > 1) {
				commonGcd = gcd(commonGcd, arr[i - 1]);
			} else {
				commonGcd = arr[0];
			}
		}
	}
	
	private static void init900000(){
		int[] a = new int[]{900001, 900007, 900019, 900037, 900061, 900089, 900091, 900103, 900121, 900139, 900143, 900149, 900157, 900161, 900169, 900187, 900217, 900233, 900241, 900253, 900259, 900283, 900287, 900293, 900307, 900329, 900331, 900349, 900397, 900409, 900443, 900461, 900481, 900491, 900511, 900539, 900551, 900553, 900563, 900569, 900577, 900583, 900587, 900589, 900593, 900607, 900623, 900649, 900659, 900671, 900673, 900689, 900701, 900719, 900737, 900743, 900751, 900761, 900763, 900773, 900797, 900803, 900817, 900821, 900863, 900869, 900917, 900929, 900931, 900937, 900959, 900971, 900973, 900997, 901007, 901009, 901013, 901063, 901067, 901079, 901093, 901097, 901111, 901133, 901141, 901169, 901171, 901177, 901183, 901193, 901207, 901211, 901213, 901247, 901249, 901253, 901273, 901279, 901309, 901333, 901339, 901367, 901399, 901403, 901423, 901427, 901429, 901441, 901447, 901451, 901457, 901471, 901489, 901499, 901501, 901513, 901517, 901529, 901547, 901567, 901591, 901613, 901643, 901657, 901679, 901687, 901709, 901717, 901739, 901741, 901751, 901781, 901787, 901811, 901819, 901841, 901861, 901891, 901907, 901909, 901919, 901931, 901937, 901963, 901973, 901993, 901997, 902009, 902017, 902029, 902039, 902047, 902053, 902087, 902089, 902119, 902137, 902141, 902179, 902191, 902201, 902227, 902261, 902263, 902281, 902299, 902303, 902311, 902333, 902347, 902351, 902357, 902389, 902401, 902413, 902437, 902449, 902471, 902477, 902483, 902501, 902507, 902521, 902563, 902569, 902579, 902591, 902597, 902599, 902611, 902639, 902653, 902659, 902669, 902677, 902687, 902719, 902723, 902753, 902761, 902767, 902771, 902777, 902789, 902807, 902821, 902827, 902849, 902873, 902903, 902933, 902953, 902963, 902971, 902977, 902981, 902987, 903017, 903029, 903037, 903073, 903079, 903103, 903109, 903143, 903151, 903163, 903179, 903197, 903211, 903223, 903251, 903257, 903269, 903311, 903323, 903337, 903347, 903359, 903367, 903389, 903391, 903403, 903407, 903421, 903443, 903449, 903451, 903457, 903479, 903493, 903527, 903541, 903547, 903563, 903569, 903607, 903613, 903641, 903649, 903673, 903677, 903691, 903701, 903709, 903751, 903757, 903761, 903781, 903803, 903827, 903841, 903871, 903883, 903899, 903913, 903919, 903949, 903967, 903979, 904019, 904027, 904049, 904067, 904069, 904073, 904087, 904093, 904097, 904103, 904117, 904121, 904147, 904157, 904181, 904193, 904201, 904207, 904217, 904219, 904261, 904283, 904289, 904297, 904303, 904357, 904361, 904369, 904399, 904441, 904459, 904483, 904489, 904499, 904511, 904513, 904517, 904523, 904531, 904559, 904573, 904577, 904601, 904619, 904627, 904633, 904637, 904643, 904661, 904663, 904667, 904679, 904681, 904693, 904697, 904721, 904727, 904733, 904759, 904769, 904777, 904781, 904789, 904793, 904801, 904811, 904823, 904847, 904861, 904867, 904873, 904879, 904901, 904903, 904907, 904919, 904931, 904933, 904987, 904997, 904999, 905011, 905053, 905059, 905071, 905083, 905087, 905111, 905123, 905137, 905143, 905147, 905161, 905167, 905171, 905189, 905197, 905207, 905209, 905213, 905227, 905249, 905269, 905291, 905297, 905299, 905329, 905339, 905347, 905381, 905413, 905449, 905453, 905461, 905477, 905491, 905497, 905507, 905551, 905581, 905587, 905599, 905617, 905621, 905629, 905647, 905651, 905659, 905677, 905683, 905687, 905693, 905701, 905713, 905719, 905759, 905761, 905767, 905783, 905803, 905819, 905833, 905843, 905897, 905909, 905917, 905923, 905951, 905959, 905963, 905999, 906007, 906011, 906013, 906023, 906029, 906043, 906089, 906107, 906119, 906121, 906133, 906179, 906187, 906197, 906203, 906211, 906229, 906233, 906259, 906263, 906289, 906293, 906313, 906317, 906329, 906331, 906343, 906349, 906371, 906377, 906383, 906391, 906403, 906421, 906427, 906431, 906461, 906473, 906481, 906487, 906497, 906517, 906523, 906539, 906541, 906557, 906589, 906601, 906613, 906617, 906641, 906649, 906673, 906679, 906691, 906701, 906707, 906713, 906727, 906749, 906751, 906757, 906767, 906779, 906793, 906809, 906817, 906823, 906839, 906847, 906869, 906881, 906901, 906911, 906923, 906929, 906931, 906943, 906949, 906973, 907019, 907021, 907031, 907063, 907073, 907099, 907111, 907133, 907139, 907141, 907163, 907169, 907183, 907199, 907211, 907213, 907217, 907223, 907229, 907237, 907259, 907267, 907279, 907297, 907301, 907321, 907331, 907363, 907367, 907369, 907391, 907393, 907397, 907399, 907427, 907433, 907447, 907457, 907469, 907471, 907481, 907493, 907507, 907513, 907549, 907561, 907567, 907583, 907589, 907637, 907651, 907657, 907663, 907667, 907691, 907693, 907703, 907717, 907723, 907727, 907733, 907757, 907759, 907793, 907807, 907811, 907813, 907831, 907843, 907849, 907871, 907891, 907909, 907913, 907927, 907957, 907967, 907969, 907997, 907999, 908003, 908041, 908053, 908057, 908071, 908081, 908101, 908113, 908129, 908137, 908153, 908179, 908183, 908197, 908213, 908221, 908233, 908249, 908287, 908317, 908321, 908353, 908359, 908363, 908377, 908381, 908417, 908419, 908441, 908449, 908459, 908471, 908489, 908491, 908503, 908513, 908521, 908527, 908533, 908539, 908543, 908549, 908573, 908581, 908591, 908597, 908603, 908617, 908623, 908627, 908653, 908669, 908671, 908711, 908723, 908731, 908741, 908749, 908759, 908771, 908797, 908807, 908813, 908819, 908821, 908849, 908851, 908857, 908861, 908863, 908879, 908881, 908893, 908909, 908911, 908927, 908953, 908959, 908993, 909019, 909023, 909031, 909037, 909043, 909047, 909061, 909071, 909089, 909091, 909107, 909113, 909119, 909133, 909151, 909173, 909203, 909217, 909239, 909241, 909247, 909253, 909281, 909287, 909289, 909299, 909301, 909317, 909319, 909329, 909331, 909341, 909343, 909371, 909379, 909383, 909401, 909409, 909437, 909451, 909457, 909463, 909481, 909521, 909529, 909539, 909541, 909547, 909577, 909599, 909611, 909613, 909631, 909637, 909679, 909683, 909691, 909697, 909731, 909737, 909743, 909761, 909767, 909773, 909787, 909791, 909803, 909809, 909829, 909833, 909859, 909863, 909877, 909889, 909899, 909901, 909907, 909911, 909917, 909971, 909973, 909977, 910003, 910031, 910051, 910069, 910093, 910097, 910099, 910103, 910109, 910121, 910127, 910139, 910141, 910171, 910177, 910199, 910201, 910207, 910213, 910219, 910229, 910277, 910279, 910307, 910361, 910369, 910421, 910447, 910451, 910453, 910457, 910471, 910519, 910523, 910561, 910577, 910583, 910603, 910619, 910621, 910627, 910631, 910643, 910661, 910691, 910709, 910711, 910747, 910751, 910771, 910781, 910787, 910799, 910807, 910817, 910849, 910853, 910883, 910909, 910939, 910957, 910981, 911003, 911011, 911023, 911033, 911039, 911063, 911077, 911087, 911089, 911101, 911111, 911129, 911147, 911159, 911161, 911167, 911171, 911173, 911179, 911201, 911219, 911227, 911231, 911233, 911249, 911269, 911291, 911293, 911303, 911311, 911321, 911327, 911341, 911357, 911359, 911363, 911371, 911413, 911419, 911437, 911453, 911459, 911503, 911507, 911527, 911549};
		for(int i = 0,len=a.length;i<len;i++){
			prime.add(a[i]);
			primeMap.put(a[i], true);
		}
	}
	private static void init800000(){
		int[] a = new int[]{800011, 800029, 800053, 800057, 800077, 800083, 800089, 800113, 800117, 800119, 800123, 800131, 800143, 800159, 800161, 800171, 800209, 800213, 800221, 800231, 800237, 800243, 800281, 800287, 800291, 800311, 800329, 800333, 800351, 800357, 800399, 800407, 800417, 800419, 800441, 800447, 800473, 800477, 800483, 800497, 800509, 800519, 800521, 800533, 800537, 800539, 800549, 800557, 800573, 800587, 800593, 800599, 800621, 800623, 800647, 800651, 800659, 800663, 800669, 800677, 800687, 800693, 800707, 800711, 800729, 800731, 800741, 800743, 800759, 800773, 800783, 800801, 800861, 800873, 800879, 800897, 800903, 800909, 800923, 800953, 800959, 800971, 800977, 800993, 800999, 801001, 801007, 801011, 801019, 801037, 801061, 801077, 801079, 801103, 801107, 801127, 801137, 801179, 801187, 801197, 801217, 801247, 801277, 801289, 801293, 801301, 801331, 801337, 801341, 801349, 801371, 801379, 801403, 801407, 801419, 801421, 801461, 801469, 801487, 801503, 801517, 801539, 801551, 801557, 801569, 801571, 801607, 801611, 801617, 801631, 801641, 801677, 801683, 801701, 801707, 801709, 801733, 801761, 801791, 801809, 801811, 801817, 801833, 801841, 801859, 801883, 801947, 801949, 801959, 801973, 801989, 802007, 802019, 802027, 802031, 802037, 802073, 802103, 802121, 802127, 802129, 802133, 802141, 802147, 802159, 802163, 802177, 802181, 802183, 802189, 802231, 802253, 802279, 802283, 802297, 802331, 802339, 802357, 802387, 802421, 802441, 802453, 802463, 802471, 802499, 802511, 802523, 802531, 802573, 802583, 802589, 802597, 802603, 802609, 802643, 802649, 802651, 802661, 802667, 802709, 802721, 802729, 802733, 802751, 802759, 802777, 802783, 802787, 802793, 802799, 802811, 802829, 802831, 802873, 802909, 802913, 802933, 802951, 802969, 802979, 802987, 803027, 803041, 803053, 803057, 803059, 803087, 803093, 803119, 803141, 803171, 803189, 803207, 803227, 803237, 803251, 803269, 803273, 803287, 803311, 803323, 803333, 803347, 803359, 803389, 803393, 803399, 803417, 803441, 803443, 803447, 803449, 803461, 803479, 803483, 803497, 803501, 803513, 803519, 803549, 803587, 803591, 803609, 803611, 803623, 803629, 803651, 803659, 803669, 803687, 803717, 803729, 803731, 803741, 803749, 803813, 803819, 803849, 803857, 803867, 803893, 803897, 803911, 803921, 803927, 803939, 803963, 803977, 803987, 803989, 804007, 804017, 804031, 804043, 804059, 804073, 804077, 804091, 804107, 804113, 804119, 804127, 804157, 804161, 804179, 804191, 804197, 804203, 804211, 804239, 804259, 804281, 804283, 804313, 804317, 804329, 804337, 804341, 804367, 804371, 804383, 804409, 804443, 804449, 804473, 804493, 804497, 804511, 804521, 804523, 804541, 804553, 804571, 804577, 804581, 804589, 804607, 804611, 804613, 804619, 804653, 804689, 804697, 804703, 804709, 804743, 804751, 804757, 804761, 804767, 804803, 804823, 804829, 804833, 804847, 804857, 804877, 804889, 804893, 804901, 804913, 804919, 804929, 804941, 804943, 804983, 804989, 804997, 805019, 805027, 805031, 805033, 805037, 805061, 805067, 805073, 805081, 805097, 805099, 805109, 805111, 805121, 805153, 805159, 805177, 805187, 805213, 805219, 805223, 805241, 805249, 805267, 805271, 805279, 805289, 805297, 805309, 805313, 805327, 805331, 805333, 805339, 805369, 805381, 805397, 805403, 805421, 805451, 805463, 805471, 805487, 805499, 805501, 805507, 805517, 805523, 805531, 805537, 805559, 805573, 805583, 805589, 805633, 805639, 805687, 805703, 805711, 805723, 805729, 805741, 805757, 805789, 805799, 805807, 805811, 805843, 805853, 805859, 805867, 805873, 805877, 805891, 805901, 805913, 805933, 805967, 805991, 806009, 806011, 806017, 806023, 806027, 806033, 806041, 806051, 806059, 806087, 806107, 806111, 806129, 806137, 806153, 806159, 806177, 806203, 806213, 806233, 806257, 806261, 806263, 806269, 806291, 806297, 806317, 806329, 806363, 806369, 806371, 806381, 806383, 806389, 806447, 806453, 806467, 806483, 806503, 806513, 806521, 806543, 806549, 806579, 806581, 806609, 806639, 806657, 806671, 806719, 806737, 806761, 806783, 806789, 806791, 806801, 806807, 806821, 806857, 806893, 806903, 806917, 806929, 806941, 806947, 806951, 806977, 806999, 807011, 807017, 807071, 807077, 807083, 807089, 807097, 807113, 807119, 807127, 807151, 807181, 807187, 807193, 807197, 807203, 807217, 807221, 807241, 807251, 807259, 807281, 807299, 807337, 807371, 807379, 807383, 807403, 807407, 807409, 807419, 807427, 807463, 807473, 807479, 807487, 807491, 807493, 807509, 807511, 807523, 807539, 807559, 807571, 807607, 807613, 807629, 807637, 807647, 807689, 807707, 807731, 807733, 807749, 807757, 807787, 807797, 807809, 807817, 807869, 807871, 807901, 807907, 807923, 807931, 807941, 807943, 807949, 807973, 807997, 808019, 808021, 808039, 808081, 808097, 808111, 808147, 808153, 808169, 808177, 808187, 808211, 808217, 808229, 808237, 808261, 808267, 808307, 808309, 808343, 808349, 808351, 808361, 808363, 808369, 808373, 808391, 808399, 808417, 808421, 808439, 808441, 808459, 808481, 808517, 808523, 808553, 808559, 808579, 808589, 808597, 808601, 808603, 808627, 808637, 808651, 808679, 808681, 808693, 808699, 808721, 808733, 808739, 808747, 808751, 808771, 808777, 808789, 808793, 808837, 808853, 808867, 808919, 808937, 808957, 808961, 808981, 808991, 808993, 809023, 809041, 809051, 809063, 809087, 809093, 809101, 809141, 809143, 809147, 809173, 809177, 809189, 809201, 809203, 809213, 809231, 809239, 809243, 809261, 809269, 809273, 809297, 809309, 809323, 809339, 809357, 809359, 809377, 809383, 809399, 809401, 809407, 809423, 809437, 809443, 809447, 809453, 809461, 809491, 809507, 809521, 809527, 809563, 809569, 809579, 809581, 809587, 809603, 809629, 809701, 809707, 809719, 809729, 809737, 809741, 809747, 809749, 809759, 809771, 809779, 809797, 809801, 809803, 809821, 809827, 809833, 809839, 809843, 809869, 809891, 809903, 809909, 809917, 809929, 809981, 809983, 809993, 810013, 810023, 810049, 810053, 810059, 810071, 810079, 810091, 810109, 810137, 810149, 810151, 810191, 810193, 810209, 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878359, 878377, 878387, 878411, 878413, 878419, 878443, 878453, 878467, 878489, 878513, 878539, 878551, 878567, 878573, 878593, 878597, 878609, 878621, 878629, 878641, 878651, 878659, 878663, 878677, 878681, 878699, 878719, 878737, 878743, 878749, 878777, 878783, 878789, 878797, 878821, 878831, 878833, 878837, 878851, 878863, 878869, 878873, 878893, 878929, 878939, 878953, 878957, 878987, 878989, 879001, 879007, 879023, 879031, 879061, 879089, 879097, 879103, 879113, 879119, 879133, 879143, 879167, 879169, 879181, 879199, 879227, 879239, 879247, 879259, 879269, 879271, 879283, 879287, 879299, 879331, 879341, 879343, 879353, 879371, 879391, 879401, 879413, 879449, 879457, 879493, 879523, 879533, 879539, 879553, 879581, 879583, 879607, 879617, 879623, 879629, 879649, 879653, 879661, 879667, 879673, 879679, 879689, 879691, 879701, 879707, 879709, 879713, 879721, 879743, 879797, 879799, 879817, 879821, 879839, 879859, 879863, 879881, 879917, 879919, 879941, 879953, 879961, 879973, 879979, 880001, 880007, 880021, 880027, 880031, 880043, 880057, 880067, 880069, 880091, 880097, 880109, 880127, 880133, 880151, 880153, 880199, 880211, 880219, 880223, 880247, 880249, 880259, 880283, 880301, 880303, 880331, 880337, 880343, 880349, 880361, 880367, 880409, 880421, 880423, 880427, 880483, 880487, 880513, 880519, 880531, 880541, 880543, 880553, 880559, 880571, 880573, 880589, 880603, 880661, 880667, 880673, 880681, 880687, 880699, 880703, 880709, 880723, 880727, 880729, 880751, 880793, 880799, 880801, 880813, 880819, 880823, 880853, 880861, 880871, 880883, 880903, 880907, 880909, 880939, 880949, 880951, 880961, 880981, 880993, 881003, 881009, 881017, 881029, 881057, 881071, 881077, 881099, 881119, 881141, 881143, 881147, 881159, 881171, 881173, 881191, 881197, 881207, 881219, 881233, 881249, 881269, 881273, 881311, 881317, 881327, 881333, 881351, 881357, 881369, 881393, 881407, 881411, 881417, 881437, 881449, 881471, 881473, 881477, 881479, 881509, 881527, 881533, 881537, 881539, 881591, 881597, 881611, 881641, 881663, 881669, 881681, 881707, 881711, 881729, 881743, 881779, 881813, 881833, 881849, 881897, 881899, 881911, 881917, 881939, 881953, 881963, 881983, 881987, 882017, 882019, 882029, 882031, 882047, 882061, 882067, 882071, 882083, 882103, 882139, 882157, 882169, 882173, 882179, 882187, 882199, 882239, 882241, 882247, 882251, 882253, 882263, 882289, 882313, 882359, 882367, 882377, 882389, 882391, 882433, 882439, 882449, 882451, 882461, 882481, 882491, 882517, 882529, 882551, 882571, 882577, 882587, 882593, 882599, 882617, 882631, 882653, 882659, 882697, 882701, 882703, 882719, 882727, 882733, 882751, 882773, 882779, 882823, 882851, 882863, 882877, 882881, 882883, 882907, 882913, 882923, 882943, 882953, 882961, 882967, 882979, 883013, 883049, 883061, 883073, 883087, 883093, 883109, 883111, 883117, 883121, 883163, 883187, 883193, 883213, 883217, 883229, 883231, 883237, 883241, 883247, 883249, 883273, 883279, 883307, 883327, 883331, 883339, 883343, 883357, 883391, 883397, 883409, 883411, 883423, 883429, 883433, 883451, 883471, 883483, 883489, 883517, 883537, 883549, 883577, 883579, 883613, 883621, 883627, 883639, 883661, 883667, 883691, 883697, 883699, 883703, 883721, 883733, 883739, 883763, 883777, 883781, 883783, 883807, 883871, 883877, 883889, 883921, 883933, 883963, 883969, 883973, 883979, 883991, 884003, 884011, 884029, 884057, 884069, 884077, 884087, 884111, 884129, 884131, 884159, 884167, 884171, 884183, 884201, 884227, 884231, 884243, 884251, 884267, 884269, 884287, 884293, 884309, 884311, 884321, 884341, 884353, 884363, 884369, 884371, 884417, 884423, 884437, 884441, 884453, 884483, 884489, 884491, 884497, 884501, 884537, 884573, 884579, 884591, 884593, 884617, 884651, 884669, 884693, 884699, 884717, 884743, 884789, 884791, 884803, 884813, 884827, 884831, 884857, 884881, 884899, 884921, 884951, 884959, 884977, 884981, 884987, 884999, 885023, 885041, 885061, 885083, 885091, 885097, 885103, 885107, 885127, 885133, 885161, 885163, 885169, 885187, 885217, 885223, 885233, 885239, 885251, 885257, 885263, 885289, 885301, 885307, 885331, 885359, 885371, 885383, 885389, 885397, 885403, 885421, 885427, 885449, 885473, 885487, 885497, 885503, 885509, 885517, 885529, 885551, 885553, 885589, 885607, 885611, 885623, 885679, 885713, 885721, 885727, 885733, 885737, 885769, 885791, 885793, 885803, 885811, 885821, 885823, 885839, 885869, 885881, 885883, 885889, 885893, 885919, 885923, 885931, 885943, 885947, 885959, 885961, 885967, 885971, 885977, 885991, 886007, 886013, 886019, 886021, 886031, 886043, 886069, 886097, 886117, 886129, 886163, 886177, 886181, 886183, 886189, 886199, 886241, 886243, 886247, 886271, 886283, 886307, 886313, 886337, 886339, 886349, 886367, 886381, 886387, 886421, 886427, 886429, 886433, 886453, 886463, 886469, 886471, 886493, 886511, 886517, 886519, 886537, 886541, 886547, 886549, 886583, 886591, 886607, 886609, 886619, 886643, 886651, 886663, 886667, 886741, 886747, 886751, 886759, 886777, 886793, 886799, 886807, 886819, 886859, 886867, 886891, 886909, 886913, 886967, 886969, 886973, 886979, 886981, 886987, 886993, 886999, 887017, 887057, 887059, 887069, 887093, 887101, 887113, 887141, 887143, 887153, 887171, 887177, 887191, 887203, 887233, 887261, 887267, 887269, 887291, 887311, 887323, 887333, 887377, 887387, 887399, 887401, 887423, 887441, 887449, 887459, 887479, 887483, 887503, 887533, 887543, 887567, 887569, 887573, 887581, 887599, 887617, 887629, 887633, 887641, 887651, 887657, 887659, 887669, 887671, 887681, 887693, 887701, 887707, 887717, 887743, 887749, 887759, 887819, 887827, 887837, 887839, 887849, 887867, 887903, 887911, 887921, 887923, 887941, 887947, 887987, 887989, 888001, 888011, 888047, 888059, 888061, 888077, 888091, 888103, 888109, 888133, 888143, 888157, 888161, 888163, 888179, 888203, 888211, 888247, 888257, 888263, 888271, 888287, 888313, 888319, 888323, 888359, 888361, 888373, 888389, 888397, 888409, 888413, 888427, 888431, 888443, 888451, 888457, 888469, 888479, 888493, 888499, 888533, 888541, 888557, 888623, 888631, 888637, 888653, 888659, 888661, 888683, 888689, 888691, 888721, 888737, 888751, 888761, 888773, 888779, 888781, 888793, 888799, 888809, 888827, 888857, 888869, 888871, 888887, 888917, 888919, 888931, 888959, 888961, 888967, 888983, 888989, 888997, 889001, 889027, 889037, 889039, 889043, 889051, 889069, 889081, 889087, 889123, 889139, 889171, 889177, 889211, 889237, 889247, 889261, 889271, 889279, 889289, 889309, 889313, 889327, 889337, 889349, 889351, 889363, 889367, 889373, 889391, 889411, 889429, 889439, 889453, 889481, 889489, 889501, 889519, 889579, 889589, 889597, 889631, 889639, 889657, 889673, 889687, 889697, 889699, 889703, 889727, 889747, 889769, 889783, 889829, 889871, 889873, 889877, 889879, 889891, 889901, 889907, 889909, 889921, 889937, 889951, 889957, 889963, 889997, 890003, 890011, 890027, 890053, 890063, 890083, 890107, 890111, 890117, 890119, 890129, 890147, 890159, 890161, 890177, 890221, 890231, 890237, 890287, 890291, 890303, 890317, 890333, 890371, 890377, 890419, 890429, 890437, 890441, 890459, 890467, 890501, 890531, 890543, 890551, 890563, 890597, 890609, 890653, 890657, 890671, 890683, 890707, 890711, 890717, 890737, 890761, 890789, 890797, 890803, 890809, 890821, 890833, 890843, 890861, 890863, 890867, 890881, 890887, 890893, 890927, 890933, 890941, 890957, 890963, 890969, 890993, 890999, 891001, 891017, 891047, 891049, 891061, 891067, 891091, 891101, 891103, 891133, 891151, 891161, 891173, 891179, 891223, 891239, 891251, 891277, 891287, 891311, 891323, 891329, 891349, 891377, 891379, 891389, 891391, 891409, 891421, 891427, 891439, 891481, 891487, 891491, 891493, 891509, 891521, 891523, 891551, 891557, 891559, 891563, 891571, 891577, 891587, 891593, 891601, 891617, 891629, 891643, 891647, 891659, 891661, 891677, 891679, 891707, 891743, 891749, 891763, 891767, 891797, 891799, 891809, 891817, 891823, 891827, 891829, 891851, 891859, 891887, 891889, 891893, 891899, 891907, 891923, 891929, 891967, 891983, 891991, 891997, 892019, 892027, 892049, 892057, 892079, 892091, 892093, 892097, 892103, 892123, 892141, 892153, 892159, 892169, 892189, 892219, 892237, 892249, 892253, 892261, 892267, 892271, 892291, 892321, 892351, 892357, 892387, 892391, 892421, 892433, 892439, 892457, 892471, 892481, 892513, 892523, 892531, 892547, 892553, 892559, 892579, 892597, 892603, 892609, 892627, 892643, 892657, 892663, 892667, 892709, 892733, 892747, 892757, 892763, 892777, 892781, 892783, 892817, 892841, 892849, 892861, 892877, 892901, 892919, 892933, 892951, 892973, 892987, 892999, 893003, 893023, 893029, 893033, 893041, 893051, 893059, 893093, 893099, 893107, 893111, 893117, 893119, 893131, 893147, 893149, 893161, 893183, 893213, 893219, 893227, 893237, 893257, 893261, 893281, 893317, 893339, 893341, 893351, 893359, 893363, 893381, 893383, 893407, 893413, 893419, 893429, 893441, 893449, 893479, 893489, 893509, 893521, 893549, 893567, 893591, 893603, 893609, 893653, 893657, 893671, 893681, 893701, 893719, 893723, 893743, 893777, 893797, 893821, 893839, 893857, 893863, 893873, 893881, 893897, 893903, 893917, 893929, 893933, 893939, 893989, 893999, 894011, 894037, 894059, 894067, 894073, 894097, 894109, 894119, 894137, 894139, 894151, 894161, 894167, 894181, 894191, 894193, 894203, 894209, 894211, 894221, 894227, 894233, 894239, 894247, 894259, 894277, 894281, 894287, 894301, 894329, 894343, 894371, 894391, 894403, 894407, 894409, 894419, 894427, 894431, 894449, 894451, 894503, 894511, 894521, 894527, 894541, 894547, 894559, 894581, 894589, 894611, 894613, 894637, 894643, 894667, 894689, 894709, 894713, 894721, 894731, 894749, 894763, 894779, 894791, 894793, 894811, 894869, 894871, 894893, 894917, 894923, 894947, 894973, 894997, 895003, 895007, 895009, 895039, 895049, 895051, 895079, 895087, 895127, 895133, 895151, 895157, 895159, 895171, 895189, 895211, 895231, 895241, 895243, 895247, 895253, 895277, 895283, 895291, 895309, 895313, 895319, 895333, 895343, 895351, 895357, 895361, 895387, 895393, 895421, 895423, 895457, 895463, 895469, 895471, 895507, 895529, 895553, 895571, 895579, 895591, 895613, 895627, 895633, 895649, 895651, 895667, 895669, 895673, 895681, 895691, 895703, 895709, 895721, 895729, 895757, 895771, 895777, 895787, 895789, 895799, 895801, 895813, 895823, 895841, 895861, 895879, 895889, 895901, 895903, 895913, 895927, 895933, 895957, 895987, 896003, 896009, 896047, 896069, 896101, 896107, 896111, 896113, 896123, 896143, 896167, 896191, 896201, 896263, 896281, 896293, 896297, 896299, 896323, 896327, 896341, 896347, 896353, 896369, 896381, 896417, 896443, 896447, 896449, 896453, 896479, 896491, 896509, 896521, 896531, 896537, 896543, 896549, 896557, 896561, 896573, 896587, 896617, 896633, 896647, 896669, 896677, 896681, 896717, 896719, 896723, 896771, 896783, 896803, 896837, 896867, 896879, 896897, 896921, 896927, 896947, 896953, 896963, 896983, 897007, 897011, 897019, 897049, 897053, 897059, 897067, 897077, 897101, 897103, 897119, 897133, 897137, 897157, 897163, 897191, 897223, 897229, 897241, 897251, 897263, 897269, 897271, 897301, 897307, 897317, 897319, 897329, 897349, 897359, 897373, 897401, 897433, 897443, 897461, 897467, 897469, 897473, 897497, 897499, 897517, 897527, 897553, 897557, 897563, 897571, 897577, 897581, 897593, 897601, 897607, 897629, 897647, 897649, 897671, 897691, 897703, 897707, 897709, 897727, 897751, 897779, 897781, 897817, 897829, 897847, 897877, 897881, 897887, 897899, 897907, 897931, 897947, 897971, 897983, 898013, 898019, 898033, 898063, 898067, 898069, 898091, 898097, 898109, 898129, 898133, 898147, 898153, 898171, 898181, 898189, 898199, 898211, 898213, 898223, 898231, 898241, 898243, 898253, 898259, 898279, 898283, 898291, 898307, 898319, 898327, 898361, 898369, 898409, 898421, 898423, 898427, 898439, 898459, 898477, 898481, 898483, 898493, 898519, 898523, 898543, 898549, 898553, 898561, 898607, 898613, 898621, 898661, 898663, 898669, 898673, 898691, 898717, 898727, 898753, 898763, 898769, 898787, 898813, 898819, 898823, 898853, 898867, 898873, 898889, 898897, 898921, 898927, 898951, 898981, 898987, 899009, 899051, 899057, 899069, 899123, 899149, 899153, 899159, 899161, 899177, 899179, 899183, 899189, 899209, 899221, 899233, 899237, 899263, 899273, 899291, 899309, 899321, 899387, 899401, 899413, 899429, 899447, 899467, 899473, 899477, 899491, 899519, 899531, 899537, 899611, 899617, 899659, 899671, 899681, 899687, 899693, 899711, 899719, 899749, 899753, 899761, 899779, 899791, 899807, 899831, 899849, 899851, 899863, 899881, 899891, 899893, 899903, 899917, 899939, 899971, 899981};
		for(int i = 0,len=a.length;i<len;i++){
			prime.add(a[i]);
			primeMap.put(a[i], true);
		}
	}
	private static void init700000(){
		int[] a = new int[]{700001, 700027, 700057, 700067, 700079, 700081, 700087, 700099, 700103, 700109, 700127, 700129, 700171, 700199, 700201, 700211, 700223, 700229, 700237, 700241, 700277, 700279, 700303, 700307, 700319, 700331, 700339, 700361, 700363, 700367, 700387, 700391, 700393, 700423, 700429, 700433, 700459, 700471, 700499, 700523, 700537, 700561, 700571, 700573, 700577, 700591, 700597, 700627, 700633, 700639, 700643, 700673, 700681, 700703, 700717, 700751, 700759, 700781, 700789, 700801, 700811, 700831, 700837, 700849, 700871, 700877, 700883, 700897, 700907, 700919, 700933, 700937, 700949, 700963, 700993, 701009, 701011, 701023, 701033, 701047, 701089, 701117, 701147, 701159, 701177, 701179, 701209, 701219, 701221, 701227, 701257, 701279, 701291, 701299, 701329, 701341, 701357, 701359, 701377, 701383, 701399, 701401, 701413, 701417, 701419, 701443, 701447, 701453, 701473, 701479, 701489, 701497, 701507, 701509, 701527, 701531, 701549, 701579, 701581, 701593, 701609, 701611, 701621, 701627, 701629, 701653, 701669, 701671, 701681, 701699, 701711, 701719, 701731, 701741, 701761, 701783, 701791, 701819, 701837, 701863, 701881, 701903, 701951, 701957, 701963, 701969, 702007, 702011, 702017, 702067, 702077, 702101, 702113, 702127, 702131, 702137, 702139, 702173, 702179, 702193, 702199, 702203, 702211, 702239, 702257, 702269, 702281, 702283, 702311, 702313, 702323, 702329, 702337, 702341, 702347, 702349, 702353, 702379, 702391, 702407, 702413, 702431, 702433, 702439, 702451, 702469, 702497, 702503, 702511, 702517, 702523, 702529, 702539, 702551, 702557, 702587, 702589, 702599, 702607, 702613, 702623, 702671, 702679, 702683, 702701, 702707, 702721, 702731, 702733, 702743, 702773, 702787, 702803, 702809, 702817, 702827, 702847, 702851, 702853, 702869, 702881, 702887, 702893, 702913, 702937, 702983, 702991, 703013, 703033, 703039, 703081, 703117, 703121, 703123, 703127, 703139, 703141, 703169, 703193, 703211, 703217, 703223, 703229, 703231, 703243, 703249, 703267, 703277, 703301, 703309, 703321, 703327, 703331, 703349, 703357, 703379, 703393, 703411, 703441, 703447, 703459, 703463, 703471, 703489, 703499, 703531, 703537, 703559, 703561, 703631, 703643, 703657, 703663, 703673, 703679, 703691, 703699, 703709, 703711, 703721, 703733, 703753, 703763, 703789, 703819, 703837, 703849, 703861, 703873, 703883, 703897, 703903, 703907, 703943, 703949, 703957, 703981, 703991, 704003, 704009, 704017, 704023, 704027, 704029, 704059, 704069, 704087, 704101, 704111, 704117, 704131, 704141, 704153, 704161, 704177, 704183, 704189, 704213, 704219, 704233, 704243, 704251, 704269, 704279, 704281, 704287, 704299, 704303, 704309, 704321, 704357, 704393, 704399, 704419, 704441, 704447, 704449, 704453, 704461, 704477, 704507, 704521, 704527, 704549, 704551, 704567, 704569, 704579, 704581, 704593, 704603, 704617, 704647, 704657, 704663, 704681, 704687, 704713, 704719, 704731, 704747, 704761, 704771, 704777, 704779, 704783, 704797, 704801, 704807, 704819, 704833, 704839, 704849, 704857, 704861, 704863, 704867, 704897, 704929, 704933, 704947, 704983, 704989, 704993, 704999, 705011, 705013, 705017, 705031, 705043, 705053, 705073, 705079, 705097, 705113, 705119, 705127, 705137, 705161, 705163, 705167, 705169, 705181, 705191, 705197, 705209, 705247, 705259, 705269, 705277, 705293, 705307, 705317, 705389, 705403, 705409, 705421, 705427, 705437, 705461, 705491, 705493, 705499, 705521, 705533, 705559, 705613, 705631, 705643, 705689, 705713, 705737, 705751, 705763, 705769, 705779, 705781, 705787, 705821, 705827, 705829, 705833, 705841, 705863, 705871, 705883, 705899, 705919, 705937, 705949, 705967, 705973, 705989, 706001, 706003, 706009, 706019, 706033, 706039, 706049, 706051, 706067, 706099, 706109, 706117, 706133, 706141, 706151, 706157, 706159, 706183, 706193, 706201, 706207, 706213, 706229, 706253, 706267, 706283, 706291, 706297, 706301, 706309, 706313, 706337, 706357, 706369, 706373, 706403, 706417, 706427, 706463, 706481, 706487, 706499, 706507, 706523, 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777641, 777643, 777661, 777671, 777677, 777683, 777731, 777737, 777743, 777761, 777769, 777781, 777787, 777817, 777839, 777857, 777859, 777863, 777871, 777877, 777901, 777911, 777919, 777977, 777979, 777989, 778013, 778027, 778049, 778051, 778061, 778079, 778081, 778091, 778097, 778109, 778111, 778121, 778123, 778153, 778163, 778187, 778201, 778213, 778223, 778237, 778241, 778247, 778301, 778307, 778313, 778319, 778333, 778357, 778361, 778363, 778391, 778397, 778403, 778409, 778417, 778439, 778469, 778507, 778511, 778513, 778523, 778529, 778537, 778541, 778553, 778559, 778567, 778579, 778597, 778633, 778643, 778663, 778667, 778681, 778693, 778697, 778699, 778709, 778717, 778727, 778733, 778759, 778763, 778769, 778777, 778793, 778819, 778831, 778847, 778871, 778873, 778879, 778903, 778907, 778913, 778927, 778933, 778951, 778963, 778979, 778993, 779003, 779011, 779021, 779039, 779063, 779069, 779081, 779101, 779111, 779131, 779137, 779159, 779173, 779189, 779221, 779231, 779239, 779249, 779267, 779327, 779329, 779341, 779347, 779351, 779353, 779357, 779377, 779413, 779477, 779489, 779507, 779521, 779531, 779543, 779561, 779563, 779573, 779579, 779591, 779593, 779599, 779609, 779617, 779621, 779657, 779659, 779663, 779693, 779699, 779707, 779731, 779747, 779749, 779761, 779767, 779771, 779791, 779797, 779827, 779837, 779869, 779873, 779879, 779887, 779899, 779927, 779939, 779971, 779981, 779983, 779993, 780029, 780037, 780041, 780047, 780049, 780061, 780119, 780127, 780163, 780173, 780179, 780191, 780193, 780211, 780223, 780233, 780253, 780257, 780287, 780323, 780343, 780347, 780371, 780379, 780383, 780389, 780397, 780401, 780421, 780433, 780457, 780469, 780499, 780523, 780553, 780583, 780587, 780601, 780613, 780631, 780649, 780667, 780671, 780679, 780683, 780697, 780707, 780719, 780721, 780733, 780799, 780803, 780809, 780817, 780823, 780833, 780841, 780851, 780853, 780869, 780877, 780887, 780889, 780917, 780931, 780953, 780961, 780971, 780973, 780991, 781003, 781007, 781021, 781043, 781051, 781063, 781069, 781087, 781111, 781117, 781127, 781129, 781139, 781163, 781171, 781199, 781211, 781217, 781229, 781243, 781247, 781271, 781283, 781301, 781307, 781309, 781321, 781327, 781351, 781357, 781367, 781369, 781387, 781397, 781399, 781409, 781423, 781427, 781433, 781453, 781481, 781483, 781493, 781511, 781513, 781519, 781523, 781531, 781559, 781567, 781589, 781601, 781607, 781619, 781631, 781633, 781661, 781673, 781681, 781721, 781733, 781741, 781771, 781799, 781801, 781817, 781819, 781853, 781861, 781867, 781883, 781889, 781897, 781919, 781951, 781961, 781967, 781969, 781973, 781987, 781997, 781999, 782003, 782009, 782011, 782053, 782057, 782071, 782083, 782087, 782107, 782113, 782123, 782129, 782137, 782141, 782147, 782149, 782183, 782189, 782191, 782209, 782219, 782231, 782251, 782263, 782267, 782297, 782311, 782329, 782339, 782371, 782381, 782387, 782389, 782393, 782429, 782443, 782461, 782473, 782489, 782497, 782501, 782519, 782539, 782581, 782611, 782641, 782659, 782669, 782671, 782687, 782689, 782707, 782711, 782723, 782777, 782783, 782791, 782839, 782849, 782861, 782891, 782911, 782921, 782941, 782963, 782981, 782983, 782993, 783007, 783011, 783019, 783023, 783043, 783077, 783089, 783119, 783121, 783131, 783137, 783143, 783149, 783151, 783191, 783193, 783197, 783227, 783247, 783257, 783259, 783269, 783283, 783317, 783323, 783329, 783337, 783359, 783361, 783373, 783379, 783407, 783413, 783421, 783473, 783487, 783527, 783529, 783533, 783553, 783557, 783569, 783571, 783599, 783613, 783619, 783641, 783647, 783661, 783677, 783689, 783691, 783701, 783703, 783707, 783719, 783721, 783733, 783737, 783743, 783749, 783763, 783767, 783779, 783781, 783787, 783791, 783793, 783799, 783803, 783829, 783869, 783877, 783931, 783953, 784009, 784039, 784061, 784081, 784087, 784097, 784103, 784109, 784117, 784129, 784153, 784171, 784181, 784183, 784211, 784213, 784219, 784229, 784243, 784249, 784283, 784307, 784309, 784313, 784321, 784327, 784349, 784351, 784367, 784373, 784379, 784387, 784409, 784411, 784423, 784447, 784451, 784457, 784463, 784471, 784481, 784489, 784501, 784513, 784541, 784543, 784547, 784561, 784573, 784577, 784583, 784603, 784627, 784649, 784661, 784687, 784697, 784717, 784723, 784727, 784753, 784789, 784799, 784831, 784837, 784841, 784859, 784867, 784897, 784913, 784919, 784939, 784957, 784961, 784981, 785003, 785017, 785033, 785053, 785093, 785101, 785107, 785119, 785123, 785129, 785143, 785153, 785159, 785167, 785203, 785207, 785219, 785221, 785227, 785249, 785269, 785287, 785293, 785299, 785303, 785311, 785321, 785329, 785333, 785341, 785347, 785353, 785357, 785363, 785377, 785413, 785423, 785431, 785459, 785461, 785483, 785501, 785503, 785527, 785537, 785549, 785569, 785573, 785579, 785591, 785597, 785623, 785627, 785641, 785651, 785671, 785693, 785717, 785731, 785737, 785753, 785773, 785777, 785779, 785801, 785803, 785809, 785839, 785857, 785861, 785879, 785903, 785921, 785923, 785947, 785951, 785963, 786001, 786013, 786017, 786031, 786047, 786053, 786059, 786061, 786077, 786109, 786127, 786151, 786167, 786173, 786179, 786197, 786211, 786223, 786241, 786251, 786271, 786307, 786311, 786319, 786329, 786337, 786349, 786371, 786407, 786419, 786431, 786433, 786449, 786469, 786491, 786547, 786551, 786553, 786587, 786589, 786613, 786629, 786659, 786661, 786673, 786691, 786697, 786701, 786703, 786707, 786719, 786739, 786763, 786803, 786823, 786829, 786833, 786859, 786881, 786887, 786889, 786901, 786931, 786937, 786941, 786949, 786959, 786971, 786979, 786983, 787021, 787043, 787051, 787057, 787067, 787069, 787079, 787091, 787099, 787123, 787139, 787153, 787181, 787187, 787207, 787217, 787243, 787261, 787277, 787289, 787309, 787331, 787333, 787337, 787357, 787361, 787427, 787429, 787433, 787439, 787447, 787469, 787477, 787483, 787489, 787513, 787517, 787519, 787529, 787537, 787541, 787547, 787573, 787601, 787609, 787621, 787639, 787649, 787667, 787697, 787711, 787747, 787751, 787757, 787769, 787771, 787777, 787783, 787793, 787807, 787811, 787817, 787823, 787837, 787879, 787883, 787903, 787907, 787939, 787973, 787981, 787993, 787999, 788009, 788023, 788027, 788033, 788041, 788071, 788077, 788087, 788089, 788093, 788107, 788129, 788153, 788159, 788167, 788173, 788189, 788209, 788213, 788231, 788261, 788267, 788287, 788309, 788317, 788321, 788351, 788353, 788357, 788363, 788369, 788377, 788383, 788387, 788393, 788399, 788413, 788419, 788429, 788449, 788467, 788479, 788497, 788521, 788527, 788531, 788537, 788549, 788561, 788563, 788569, 788603, 788621, 788651, 788659, 788677, 788687, 788701, 788719, 788761, 788779, 788789, 788813, 788819, 788849, 788863, 788867, 788869, 788873, 788891, 788897, 788903, 788927, 788933, 788941, 788947, 788959, 788971, 788993, 788999, 789001, 789017, 789029, 789031, 789067, 789077, 789091, 789097, 789101, 789109, 789121, 789133, 789137, 789149, 789169, 789181, 789221, 789227, 789251, 789311, 789323, 789331, 789343, 789367, 789377, 789389, 789391, 789407, 789419, 789443, 789473, 789491, 789493, 789511, 789527, 789533, 789557, 789571, 789577, 789587, 789589, 789611, 789623, 789631, 789653, 789671, 789673, 789683, 789689, 789709, 789713, 789721, 789731, 789739, 789749, 789793, 789823, 789829, 789847, 789851, 789857, 789883, 789941, 789959, 789961, 789967, 789977, 789979, 790003, 790021, 790033, 790043, 790051, 790057, 790063, 790087, 790093, 790099, 790121, 790169, 790171, 790189, 790199, 790201, 790219, 790241, 790261, 790271, 790277, 790289, 790291, 790327, 790331, 790333, 790351, 790369, 790379, 790397, 790403, 790417, 790421, 790429, 790451, 790459, 790481, 790501, 790513, 790519, 790523, 790529, 790547, 790567, 790583, 790589, 790607, 790613, 790633, 790637, 790649, 790651, 790693, 790697, 790703, 790709, 790733, 790739, 790747, 790753, 790781, 790793, 790817, 790819, 790831, 790843, 790861, 790871, 790879, 790883, 790897, 790927, 790957, 790961, 790967, 790969, 790991, 790997, 791003, 791009, 791017, 791029, 791047, 791053, 791081, 791093, 791099, 791111, 791117, 791137, 791159, 791191, 791201, 791209, 791227, 791233, 791251, 791257, 791261, 791291, 791309, 791311, 791317, 791321, 791347, 791363, 791377, 791387, 791411, 791419, 791431, 791443, 791447, 791473, 791489, 791519, 791543, 791561, 791563, 791569, 791573, 791599, 791627, 791629, 791657, 791663, 791677, 791699, 791773, 791783, 791789, 791797, 791801, 791803, 791827, 791849, 791851, 791887, 791891, 791897, 791899, 791909, 791927, 791929, 791933, 791951, 791969, 791971, 791993, 792023, 792031, 792037, 792041, 792049, 792061, 792067, 792073, 792101, 792107, 792109, 792119, 792131, 792151, 792163, 792179, 792223, 792227, 792229, 792241, 792247, 792257, 792263, 792277, 792283, 792293, 792299, 792301, 792307, 792317, 792359, 792371, 792377, 792383, 792397, 792413, 792443, 792461, 792479, 792481, 792487, 792521, 792529, 792551, 792553, 792559, 792563, 792581, 792593, 792601, 792613, 792629, 792637, 792641, 792643, 792647, 792667, 792679, 792689, 792691, 792697, 792703, 792709, 792713, 792731, 792751, 792769, 792793, 792797, 792821, 792871, 792881, 792893, 792907, 792919, 792929, 792941, 792959, 792973, 792983, 792989, 792991, 793043, 793069, 793099, 793103, 793123, 793129, 793139, 793159, 793181, 793187, 793189, 793207, 793229, 793253, 793279, 793297, 793301, 793327, 793333, 793337, 793343, 793379, 793399, 793439, 793447, 793453, 793487, 793489, 793493, 793511, 793517, 793519, 793537, 793547, 793553, 793561, 793591, 793601, 793607, 793621, 793627, 793633, 793669, 793673, 793691, 793699, 793711, 793717, 793721, 793733, 793739, 793757, 793769, 793777, 793787, 793789, 793813, 793841, 793843, 793853, 793867, 793889, 793901, 793927, 793931, 793939, 793957, 793967, 793979, 793981, 793999, 794009, 794011, 794023, 794033, 794039, 794041, 794063, 794071, 794077, 794089, 794111, 794113, 794119, 794137, 794141, 794149, 794153, 794161, 794173, 794179, 794191, 794201, 794203, 794207, 794221, 794231, 794239, 794249, 794327, 794341, 794363, 794383, 794389, 794399, 794407, 794413, 794449, 794471, 794473, 794477, 794483, 794491, 794509, 794531, 794537, 794543, 794551, 794557, 794569, 794579, 794587, 794593, 794641, 794653, 794657, 794659, 794669, 794693, 794711, 794741, 794743, 794749, 794779, 794831, 794879, 794881, 794887, 794921, 794923, 794953, 794957, 794993, 794999, 795001, 795007, 795023, 795071, 795077, 795079, 795083, 795097, 795101, 795103, 795121, 795127, 795139, 795149, 795161, 795187, 795203, 795211, 795217, 795233, 795239, 795251, 795253, 795299, 795307, 795323, 795329, 795337, 795343, 795349, 795427, 795449, 795461, 795467, 795479, 795493, 795503, 795517, 795527, 795533, 795539, 795551, 795581, 795589, 795601, 795643, 795647, 795649, 795653, 795659, 795661, 795667, 795679, 795703, 795709, 795713, 795727, 795737, 795761, 795763, 795791, 795793, 795797, 795799, 795803, 795827, 795829, 795871, 795877, 795913, 795917, 795931, 795937, 795941, 795943, 795947, 795979, 795983, 795997, 796001, 796009, 796063, 796067, 796091, 796121, 796139, 796141, 796151, 796171, 796177, 796181, 796189, 796193, 796217, 796247, 796259, 796267, 796291, 796303, 796307, 796337, 796339, 796361, 796363, 796373, 796379, 796387, 796391, 796409, 796447, 796451, 796459, 796487, 796493, 796517, 796531, 796541, 796553, 796561, 796567, 796571, 796583, 796591, 796619, 796633, 796657, 796673, 796687, 796693, 796699, 796709, 796711, 796751, 796759, 796769, 796777, 796781, 796799, 796801, 796813, 796819, 796847, 796849, 796853, 796867, 796871, 796877, 796889, 796921, 796931, 796933, 796937, 796951, 796967, 796969, 796981, 797003, 797009, 797021, 797029, 797033, 797039, 797051, 797053, 797057, 797063, 797077, 797119, 797131, 797143, 797161, 797171, 797201, 797207, 797273, 797281, 797287, 797309, 797311, 797333, 797353, 797359, 797383, 797389, 797399, 797417, 797429, 797473, 797497, 797507, 797509, 797539, 797549, 797551, 797557, 797561, 797567, 797569, 797579, 797581, 797591, 797593, 797611, 797627, 797633, 797647, 797681, 797689, 797701, 797711, 797729, 797743, 797747, 797767, 797773, 797813, 797833, 797851, 797869, 797887, 797897, 797911, 797917, 797933, 797947, 797957, 797977, 797987, 798023, 798043, 798059, 798067, 798071, 798079, 798089, 798097, 798101, 798121, 798131, 798139, 798143, 798151, 798173, 798179, 798191, 798197, 798199, 798221, 798223, 798227, 798251, 798257, 798263, 798271, 798293, 798319, 798331, 798373, 798383, 798397, 798403, 798409, 798443, 798451, 798461, 798481, 798487, 798503, 798517, 798521, 798527, 798533, 798569, 798599, 798613, 798641, 798647, 798649, 798667, 798691, 798697, 798701, 798713, 798727, 798737, 798751, 798757, 798773, 798781, 798799, 798823, 798871, 798887, 798911, 798923, 798929, 798937, 798943, 798961, 799003, 799021, 799031, 799061, 799063, 799091, 799093, 799103, 799147, 799151, 799171, 799217, 799219, 799223, 799259, 799291, 799301, 799303, 799307, 799313, 799333, 799343, 799361, 799363, 799369, 799417, 799427, 799441, 799453, 799471, 799481, 799483, 799489, 799507, 799523, 799529, 799543, 799553, 799573, 799609, 799613, 799619, 799621, 799633, 799637, 799651, 799657, 799661, 799679, 799723, 799727, 799739, 799741, 799753, 799759, 799789, 799801, 799807, 799817, 799837, 799853, 799859, 799873, 799891, 799921, 799949, 799961, 799979, 799991, 799993, 799999};
		for(int i = 0,len=a.length;i<len;i++){
			prime.add(a[i]);
			primeMap.put(a[i], true);
		}
	}
	private static  void init600000(){
		int[] a = new int[]{600011, 600043, 600053, 600071, 600073, 600091, 600101, 600109, 600167, 600169, 600203, 600217, 600221, 600233, 600239, 600241, 600247, 600269, 600283, 600289, 600293, 600307, 600311, 600317, 600319, 600337, 600359, 600361, 600367, 600371, 600401, 600403, 600407, 600421, 600433, 600449, 600451, 600463, 600469, 600487, 600517, 600529, 600557, 600569, 600577, 600601, 600623, 600631, 600641, 600659, 600673, 600689, 600697, 600701, 600703, 600727, 600751, 600791, 600823, 600827, 600833, 600841, 600857, 600877, 600881, 600883, 600889, 600893, 600931, 600947, 600949, 600959, 600961, 600973, 600979, 600983, 601021, 601031, 601037, 601039, 601043, 601061, 601067, 601079, 601093, 601127, 601147, 601187, 601189, 601193, 601201, 601207, 601219, 601231, 601241, 601247, 601259, 601267, 601283, 601291, 601297, 601309, 601313, 601319, 601333, 601339, 601357, 601379, 601397, 601411, 601423, 601439, 601451, 601457, 601487, 601507, 601541, 601543, 601589, 601591, 601607, 601631, 601651, 601669, 601687, 601697, 601717, 601747, 601751, 601759, 601763, 601771, 601801, 601807, 601813, 601819, 601823, 601831, 601849, 601873, 601883, 601889, 601897, 601903, 601943, 601949, 601961, 601969, 601981, 602029, 602033, 602039, 602047, 602057, 602081, 602083, 602087, 602093, 602099, 602111, 602137, 602141, 602143, 602153, 602179, 602197, 602201, 602221, 602227, 602233, 602257, 602267, 602269, 602279, 602297, 602309, 602311, 602317, 602321, 602333, 602341, 602351, 602377, 602383, 602401, 602411, 602431, 602453, 602461, 602477, 602479, 602489, 602501, 602513, 602521, 602543, 602551, 602593, 602597, 602603, 602621, 602627, 602639, 602647, 602677, 602687, 602689, 602711, 602713, 602717, 602729, 602743, 602753, 602759, 602773, 602779, 602801, 602821, 602831, 602839, 602867, 602873, 602887, 602891, 602909, 602929, 602947, 602951, 602971, 602977, 602983, 602999, 603011, 603013, 603023, 603047, 603077, 603091, 603101, 603103, 603131, 603133, 603149, 603173, 603191, 603203, 603209, 603217, 603227, 603257, 603283, 603311, 603319, 603349, 603389, 603391, 603401, 603431, 603443, 603457, 603467, 603487, 603503, 603521, 603523, 603529, 603541, 603553, 603557, 603563, 603569, 603607, 603613, 603623, 603641, 603667, 603679, 603689, 603719, 603731, 603739, 603749, 603761, 603769, 603781, 603791, 603793, 603817, 603821, 603833, 603847, 603851, 603853, 603859, 603881, 603893, 603899, 603901, 603907, 603913, 603917, 603919, 603923, 603931, 603937, 603947, 603949, 603989, 604001, 604007, 604013, 604031, 604057, 604063, 604069, 604073, 604171, 604189, 604223, 604237, 604243, 604249, 604259, 604277, 604291, 604309, 604313, 604319, 604339, 604343, 604349, 604361, 604369, 604379, 604397, 604411, 604427, 604433, 604441, 604477, 604481, 604517, 604529, 604547, 604559, 604579, 604589, 604603, 604609, 604613, 604619, 604649, 604651, 604661, 604697, 604699, 604711, 604727, 604729, 604733, 604753, 604759, 604781, 604787, 604801, 604811, 604819, 604823, 604829, 604837, 604859, 604861, 604867, 604883, 604907, 604931, 604939, 604949, 604957, 604973, 604997, 605009, 605021, 605023, 605039, 605051, 605069, 605071, 605113, 605117, 605123, 605147, 605167, 605173, 605177, 605191, 605221, 605233, 605237, 605239, 605249, 605257, 605261, 605309, 605323, 605329, 605333, 605347, 605369, 605393, 605401, 605411, 605413, 605443, 605471, 605477, 605497, 605503, 605509, 605531, 605533, 605543, 605551, 605573, 605593, 605597, 605599, 605603, 605609, 605617, 605629, 605639, 605641, 605687, 605707, 605719, 605779, 605789, 605809, 605837, 605849, 605861, 605867, 605873, 605879, 605887, 605893, 605909, 605921, 605933, 605947, 605953, 605977, 605987, 605993, 606017, 606029, 606031, 606037, 606041, 606049, 606059, 606077, 606079, 606083, 606091, 606113, 606121, 606131, 606173, 606181, 606223, 606241, 606247, 606251, 606299, 606301, 606311, 606313, 606323, 606341, 606379, 606383, 606413, 606433, 606443, 606449, 606493, 606497, 606503, 606521, 606527, 606539, 606559, 606569, 606581, 606587, 606589, 606607, 606643, 606649, 606653, 606659, 606673, 606721, 606731, 606733, 606737, 606743, 606757, 606791, 606811, 606829, 606833, 606839, 606847, 606857, 606863, 606899, 606913, 606919, 606943, 606959, 606961, 606967, 606971, 606997, 607001, 607003, 607007, 607037, 607043, 607049, 607063, 607067, 607081, 607091, 607093, 607097, 607109, 607127, 607129, 607147, 607151, 607153, 607157, 607163, 607181, 607199, 607213, 607219, 607249, 607253, 607261, 607301, 607303, 607307, 607309, 607319, 607331, 607337, 607339, 607349, 607357, 607363, 607417, 607421, 607423, 607471, 607493, 607517, 607531, 607549, 607573, 607583, 607619, 607627, 607667, 607669, 607681, 607697, 607703, 607721, 607723, 607727, 607741, 607769, 607813, 607819, 607823, 607837, 607843, 607861, 607883, 607889, 607909, 607921, 607931, 607933, 607939, 607951, 607961, 607967, 607991, 607993, 608011, 608029, 608033, 608087, 608089, 608099, 608117, 608123, 608129, 608131, 608147, 608161, 608177, 608191, 608207, 608213, 608269, 608273, 608297, 608299, 608303, 608339, 608347, 608357, 608359, 608369, 608371, 608383, 608389, 608393, 608401, 608411, 608423, 608429, 608431, 608459, 608471, 608483, 608497, 608519, 608521, 608527, 608581, 608591, 608593, 608609, 608611, 608633, 608653, 608659, 608669, 608677, 608693, 608701, 608737, 608743, 608749, 608759, 608767, 608789, 608819, 608831, 608843, 608851, 608857, 608863, 608873, 608887, 608897, 608899, 608903, 608941, 608947, 608953, 608977, 608987, 608989, 608999, 609043, 609047, 609067, 609071, 609079, 609101, 609107, 609113, 609143, 609149, 609163, 609173, 609179, 609199, 609209, 609221, 609227, 609233, 609241, 609253, 609269, 609277, 609283, 609289, 609307, 609313, 609337, 609359, 609361, 609373, 609379, 609391, 609397, 609403, 609407, 609421, 609437, 609443, 609461, 609487, 609503, 609509, 609517, 609527, 609533, 609541, 609571, 609589, 609593, 609599, 609601, 609607, 609613, 609617, 609619, 609641, 609673, 609683, 609701, 609709, 609743, 609751, 609757, 609779, 609781, 609803, 609809, 609821, 609859, 609877, 609887, 609907, 609911, 609913, 609923, 609929, 609979, 609989, 609991, 609997, 610031, 610063, 610081, 610123, 610157, 610163, 610187, 610193, 610199, 610217, 610219, 610229, 610243, 610271, 610279, 610289, 610301, 610327, 610331, 610339, 610391, 610409, 610417, 610429, 610439, 610447, 610457, 610469, 610501, 610523, 610541, 610543, 610553, 610559, 610567, 610579, 610583, 610619, 610633, 610639, 610651, 610661, 610667, 610681, 610699, 610703, 610721, 610733, 610739, 610741, 610763, 610781, 610783, 610787, 610801, 610817, 610823, 610829, 610837, 610843, 610847, 610849, 610867, 610877, 610879, 610891, 610913, 610919, 610921, 610933, 610957, 610969, 610993, 611011, 611027, 611033, 611057, 611069, 611071, 611081, 611101, 611111, 611113, 611131, 611137, 611147, 611189, 611207, 611213, 611257, 611263, 611279, 611293, 611297, 611323, 611333, 611389, 611393, 611411, 611419, 611441, 611449, 611453, 611459, 611467, 611483, 611497, 611531, 611543, 611549, 611551, 611557, 611561, 611587, 611603, 611621, 611641, 611657, 611671, 611693, 611707, 611729, 611753, 611791, 611801, 611803, 611827, 611833, 611837, 611839, 611873, 611879, 611887, 611903, 611921, 611927, 611939, 611951, 611953, 611957, 611969, 611977, 611993, 611999, 612011, 612023, 612037, 612041, 612043, 612049, 612061, 612067, 612071, 612083, 612107, 612109, 612113, 612133, 612137, 612149, 612169, 612173, 612181, 612193, 612217, 612223, 612229, 612259, 612263, 612301, 612307, 612317, 612319, 612331, 612341, 612349, 612371, 612373, 612377, 612383, 612401, 612407, 612439, 612481, 612497, 612511, 612553, 612583, 612589, 612611, 612613, 612637, 612643, 612649, 612671, 612679, 612713, 612719, 612727, 612737, 612751, 612763, 612791, 612797, 612809, 612811, 612817, 612823, 612841, 612847, 612853, 612869, 612877, 612889, 612923, 612929, 612947, 612967, 612971, 612977, 613007, 613009, 613013, 613049, 613061, 613097, 613099, 613141, 613153, 613163, 613169, 613177, 613181, 613189, 613199, 613213, 613219, 613229, 613231, 613243, 613247, 613253, 613267, 613279, 613289, 613297, 613337, 613357, 613363, 613367, 613381, 613421, 613427, 613439, 613441, 613447, 613451, 613463, 613469, 613471, 613493, 613499, 613507, 613523, 613549, 613559, 613573, 613577, 613597, 613607, 613609, 613633, 613637, 613651, 613661, 613667, 613673, 613699, 613733, 613741, 613747, 613759, 613763, 613807, 613813, 613817, 613829, 613841, 613849, 613861, 613883, 613889, 613903, 613957, 613967, 613969, 613981, 613993, 613999, 614041, 614051, 614063, 614071, 614093, 614101, 614113, 614129, 614143, 614147, 614153, 614167, 614177, 614179, 614183, 614219, 614267, 614279, 614291, 614293, 614297, 614321, 614333, 614377, 614387, 614413, 614417, 614437, 614477, 614483, 614503, 614527, 614531, 614543, 614561, 614563, 614569, 614609, 614611, 614617, 614623, 614633, 614639, 614657, 614659, 614671, 614683, 614687, 614693, 614701, 614717, 614729, 614741, 614743, 614749, 614753, 614759, 614773, 614827, 614843, 614849, 614851, 614863, 614881, 614893, 614909, 614917, 614927, 614963, 614981, 614983, 615019, 615031, 615047, 615053, 615067, 615101, 615103, 615107, 615137, 615151, 615161, 615187, 615229, 615233, 615253, 615259, 615269, 615289, 615299, 615313, 615337, 615341, 615343, 615367, 615379, 615389, 615401, 615403, 615413, 615427, 615431, 615437, 615449, 615473, 615479, 615491, 615493, 615497, 615509, 615521, 615539, 615557, 615577, 615599, 615607, 615617, 615623, 615661, 615677, 615679, 615709, 615721, 615731, 615739, 615743, 615749, 615751, 615761, 615767, 615773, 615793, 615799, 615821, 615827, 615829, 615833, 615869, 615883, 615887, 615907, 615919, 615941, 615949, 615971, 615997, 616003, 616027, 616051, 616069, 616073, 616079, 616103, 616111, 616117, 616129, 616139, 616141, 616153, 616157, 616169, 616171, 616181, 616207, 616211, 616219, 616223, 616229, 616243, 616261, 616277, 616289, 616307, 616313, 616321, 616327, 616361, 616367, 616387, 616391, 616393, 616409, 616411, 616433, 616439, 616459, 616463, 616481, 616489, 616501, 616507, 616513, 616519, 616523, 616529, 616537, 616547, 616579, 616589, 616597, 616639, 616643, 616669, 616673, 616703, 616717, 616723, 616729, 616741, 616757, 616769, 616783, 616787, 616789, 616793, 616799, 616829, 616841, 616843, 616849, 616871, 616877, 616897, 616909, 616933, 616943, 616951, 616961, 616991, 616997, 616999, 617011, 617027, 617039, 617051, 617053, 617059, 617077, 617087, 617107, 617119, 617129, 617131, 617147, 617153, 617161, 617189, 617191, 617231, 617233, 617237, 617249, 617257, 617269, 617273, 617293, 617311, 617327, 617333, 617339, 617341, 617359, 617363, 617369, 617387, 617401, 617411, 617429, 617447, 617453, 617467, 617471, 617473, 617479, 617509, 617521, 617531, 617537, 617579, 617587, 617647, 617651, 617657, 617677, 617681, 617689, 617693, 617699, 617707, 617717, 617719, 617723, 617731, 617759, 617761, 617767, 617777, 617791, 617801, 617809, 617819, 617843, 617857, 617873, 617879, 617887, 617917, 617951, 617959, 617963, 617971, 617983, 618029, 618031, 618041, 618049, 618053, 618083, 618119, 618131, 618161, 618173, 618199, 618227, 618229, 618253, 618257, 618269, 618271, 618287, 618301, 618311, 618323, 618329, 618337, 618347, 618349, 618361, 618377, 618407, 618413, 618421, 618437, 618439, 618463, 618509, 618521, 618547, 618559, 618571, 618577, 618581, 618587, 618589, 618593, 618619, 618637, 618643, 618671, 618679, 618703, 618707, 618719, 618799, 618823, 618833, 618841, 618847, 618857, 618859, 618869, 618883, 618913, 618929, 618941, 618971, 618979, 618991, 618997, 619007, 619009, 619019, 619027, 619033, 619057, 619061, 619067, 619079, 619111, 619117, 619139, 619159, 619169, 619181, 619187, 619189, 619207, 619247, 619253, 619261, 619273, 619277, 619279, 619303, 619309, 619313, 619331, 619363, 619373, 619391, 619397, 619471, 619477, 619511, 619537, 619543, 619561, 619573, 619583, 619589, 619603, 619607, 619613, 619621, 619657, 619669, 619681, 619687, 619693, 619711, 619739, 619741, 619753, 619763, 619771, 619793, 619807, 619811, 619813, 619819, 619831, 619841, 619849, 619867, 619897, 619909, 619921, 619967, 619979, 619981, 619987, 619999, 620003, 620029, 620033, 620051, 620099, 620111, 620117, 620159, 620161, 620171, 620183, 620197, 620201, 620227, 620233, 620237, 620239, 620251, 620261, 620297, 620303, 620311, 620317, 620329, 620351, 620359, 620363, 620377, 620383, 620393, 620401, 620413, 620429, 620437, 620441, 620461, 620467, 620491, 620507, 620519, 620531, 620549, 620561, 620567, 620569, 620579, 620603, 620623, 620639, 620647, 620657, 620663, 620671, 620689, 620693, 620717, 620731, 620743, 620759, 620771, 620773, 620777, 620813, 620821, 620827, 620831, 620849, 620869, 620887, 620909, 620911, 620929, 620933, 620947, 620957, 620981, 620999, 621007, 621013, 621017, 621029, 621031, 621043, 621059, 621083, 621097, 621113, 621133, 621139, 621143, 621217, 621223, 621227, 621239, 621241, 621259, 621289, 621301, 621317, 621337, 621343, 621347, 621353, 621359, 621371, 621389, 621419, 621427, 621431, 621443, 621451, 621461, 621473, 621521, 621527, 621541, 621583, 621611, 621617, 621619, 621629, 621631, 621641, 621671, 621679, 621697, 621701, 621703, 621721, 621739, 621749, 621757, 621769, 621779, 621799, 621821, 621833, 621869, 621871, 621883, 621893, 621913, 621923, 621937, 621941, 621983, 621997, 622009, 622019, 622043, 622049, 622051, 622067, 622073, 622091, 622103, 622109, 622123, 622129, 622133, 622151, 622157, 622159, 622177, 622187, 622189, 622241, 622243, 622247, 622249, 622277, 622301, 622313, 622331, 622333, 622337, 622351, 622367, 622397, 622399, 622423, 622477, 622481, 622483, 622493, 622513, 622519, 622529, 622547, 622549, 622561, 622571, 622577, 622603, 622607, 622613, 622619, 622621, 622637, 622639, 622663, 622669, 622709, 622723, 622729, 622751, 622777, 622781, 622793, 622813, 622849, 622861, 622879, 622889, 622901, 622927, 622943, 622957, 622967, 622987, 622997, 623003, 623009, 623017, 623023, 623041, 623057, 623059, 623071, 623107, 623171, 623209, 623221, 623261, 623263, 623269, 623279, 623281, 623291, 623299, 623303, 623321, 623327, 623341, 623351, 623353, 623383, 623387, 623393, 623401, 623417, 623423, 623431, 623437, 623477, 623521, 623531, 623537, 623563, 623591, 623617, 623621, 623633, 623641, 623653, 623669, 623671, 623677, 623681, 623683, 623699, 623717, 623719, 623723, 623729, 623743, 623759, 623767, 623771, 623803, 623839, 623851, 623867, 623869, 623879, 623881, 623893, 623923, 623929, 623933, 623947, 623957, 623963, 623977, 623983, 623989, 624007, 624031, 624037, 624047, 624049, 624067, 624089, 624097, 624119, 624133, 624139, 624149, 624163, 624191, 624199, 624203, 624209, 624229, 624233, 624241, 624251, 624259, 624271, 624277, 624311, 624313, 624319, 624329, 624331, 624347, 624391, 624401, 624419, 624443, 624451, 624467, 624469, 624479, 624487, 624497, 624509, 624517, 624521, 624539, 624541, 624577, 624593, 624599, 624601, 624607, 624643, 624649, 624667, 624683, 624707, 624709, 624721, 624727, 624731, 624737, 624763, 624769, 624787, 624791, 624797, 624803, 624809, 624829, 624839, 624847, 624851, 624859, 624917, 624961, 624973, 624977, 624983, 624997, 625007, 625033, 625057, 625063, 625087, 625103, 625109, 625111, 625129, 625133, 625169, 625171, 625181, 625187, 625199, 625213, 625231, 625237, 625253, 625267, 625279, 625283, 625307, 625319, 625343, 625351, 625367, 625369, 625397, 625409, 625451, 625477, 625483, 625489, 625507, 625517, 625529, 625543, 625589, 625591, 625609, 625621, 625627, 625631, 625637, 625643, 625657, 625661, 625663, 625697, 625699, 625763, 625777, 625789, 625811, 625819, 625831, 625837, 625861, 625871, 625883, 625909, 625913, 625927, 625939, 625943, 625969, 625979, 625997, 626009, 626011, 626033, 626051, 626063, 626113, 626117, 626147, 626159, 626173, 626177, 626189, 626191, 626201, 626207, 626239, 626251, 626261, 626317, 626323, 626333, 626341, 626347, 626363, 626377, 626389, 626393, 626443, 626477, 626489, 626519, 626533, 626539, 626581, 626597, 626599, 626609, 626611, 626617, 626621, 626623, 626627, 626629, 626663, 626683, 626687, 626693, 626701, 626711, 626713, 626723, 626741, 626749, 626761, 626771, 626783, 626797, 626809, 626833, 626837, 626861, 626887, 626917, 626921, 626929, 626947, 626953, 626959, 626963, 626987, 627017, 627041, 627059, 627071, 627073, 627083, 627089, 627091, 627101, 627119, 627131, 627139, 627163, 627169, 627191, 627197, 627217, 627227, 627251, 627257, 627269, 627271, 627293, 627301, 627329, 627349, 627353, 627377, 627379, 627383, 627391, 627433, 627449, 627479, 627481, 627491, 627511, 627541, 627547, 627559, 627593, 627611, 627617, 627619, 627637, 627643, 627659, 627661, 627667, 627673, 627709, 627721, 627733, 627749, 627773, 627787, 627791, 627797, 627799, 627811, 627841, 627859, 627901, 627911, 627919, 627943, 627947, 627953, 627961, 627973, 628013, 628021, 628037, 628049, 628051, 628057, 628063, 628093, 628097, 628127, 628139, 628171, 628183, 628189, 628193, 628207, 628213, 628217, 628219, 628231, 628261, 628267, 628289, 628301, 628319, 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677119, 677147, 677167, 677177, 677213, 677227, 677231, 677233, 677239, 677309, 677311, 677321, 677323, 677333, 677357, 677371, 677387, 677423, 677441, 677447, 677459, 677461, 677471, 677473, 677531, 677533, 677539, 677543, 677561, 677563, 677587, 677627, 677639, 677647, 677657, 677681, 677683, 677687, 677717, 677737, 677767, 677779, 677783, 677791, 677813, 677827, 677857, 677891, 677927, 677947, 677953, 677959, 677983, 678023, 678037, 678047, 678061, 678077, 678101, 678103, 678133, 678157, 678169, 678179, 678191, 678199, 678203, 678211, 678217, 678221, 678229, 678253, 678289, 678299, 678329, 678341, 678343, 678367, 678371, 678383, 678401, 678407, 678409, 678413, 678421, 678437, 678451, 678463, 678479, 678481, 678493, 678499, 678533, 678541, 678553, 678563, 678577, 678581, 678593, 678599, 678607, 678611, 678631, 678637, 678641, 678647, 678649, 678653, 678659, 678719, 678721, 678731, 678739, 678749, 678757, 678761, 678763, 678767, 678773, 678779, 678809, 678823, 678829, 678833, 678859, 678871, 678883, 678901, 678907, 678941, 678943, 678949, 678959, 678971, 678989, 679033, 679037, 679039, 679051, 679067, 679087, 679111, 679123, 679127, 679153, 679157, 679169, 679171, 679183, 679207, 679219, 679223, 679229, 679249, 679277, 679279, 679297, 679309, 679319, 679333, 679361, 679363, 679369, 679373, 679381, 679403, 679409, 679417, 679423, 679433, 679451, 679463, 679487, 679501, 679517, 679519, 679531, 679537, 679561, 679597, 679603, 679607, 679633, 679639, 679669, 679681, 679691, 679699, 679709, 679733, 679741, 679747, 679751, 679753, 679781, 679793, 679807, 679823, 679829, 679837, 679843, 679859, 679867, 679879, 679883, 679891, 679897, 679907, 679909, 679919, 679933, 679951, 679957, 679961, 679969, 679981, 679993, 679999, 680003, 680027, 680039, 680059, 680077, 680081, 680083, 680107, 680123, 680129, 680159, 680161, 680177, 680189, 680203, 680209, 680213, 680237, 680249, 680263, 680291, 680293, 680297, 680299, 680321, 680327, 680341, 680347, 680353, 680377, 680387, 680399, 680401, 680411, 680417, 680431, 680441, 680443, 680453, 680489, 680503, 680507, 680509, 680531, 680539, 680567, 680569, 680587, 680597, 680611, 680623, 680633, 680651, 680657, 680681, 680707, 680749, 680759, 680767, 680783, 680803, 680809, 680831, 680857, 680861, 680873, 680879, 680881, 680917, 680929, 680959, 680971, 680987, 680989, 680993, 681001, 681011, 681019, 681041, 681047, 681049, 681061, 681067, 681089, 681091, 681113, 681127, 681137, 681151, 681167, 681179, 681221, 681229, 681251, 681253, 681257, 681259, 681271, 681293, 681311, 681337, 681341, 681361, 681367, 681371, 681403, 681407, 681409, 681419, 681427, 681449, 681451, 681481, 681487, 681493, 681497, 681521, 681523, 681539, 681557, 681563, 681589, 681607, 681613, 681623, 681631, 681647, 681673, 681677, 681689, 681719, 681727, 681731, 681763, 681773, 681781, 681787, 681809, 681823, 681833, 681839, 681841, 681883, 681899, 681913, 681931, 681943, 681949, 681971, 681977, 681979, 681983, 681997, 682001, 682009, 682037, 682049, 682063, 682069, 682079, 682141, 682147, 682151, 682153, 682183, 682207, 682219, 682229, 682237, 682247, 682259, 682277, 682289, 682291, 682303, 682307, 682321, 682327, 682333, 682337, 682361, 682373, 682411, 682417, 682421, 682427, 682439, 682447, 682463, 682471, 682483, 682489, 682511, 682519, 682531, 682547, 682597, 682607, 682637, 682657, 682673, 682679, 682697, 682699, 682723, 682729, 682733, 682739, 682751, 682763, 682777, 682789, 682811, 682819, 682901, 682933, 682943, 682951, 682967, 683003, 683021, 683041, 683047, 683071, 683083, 683087, 683119, 683129, 683143, 683149, 683159, 683201, 683231, 683251, 683257, 683273, 683299, 683303, 683317, 683323, 683341, 683351, 683357, 683377, 683381, 683401, 683407, 683437, 683447, 683453, 683461, 683471, 683477, 683479, 683483, 683489, 683503, 683513, 683567, 683591, 683597, 683603, 683651, 683653, 683681, 683687, 683693, 683699, 683701, 683713, 683719, 683731, 683737, 683747, 683759, 683777, 683783, 683789, 683807, 683819, 683821, 683831, 683833, 683843, 683857, 683861, 683863, 683873, 683887, 683899, 683909, 683911, 683923, 683933, 683939, 683957, 683983, 684007, 684017, 684037, 684053, 684091, 684109, 684113, 684119, 684121, 684127, 684157, 684163, 684191, 684217, 684221, 684239, 684269, 684287, 684289, 684293, 684311, 684329, 684337, 684347, 684349, 684373, 684379, 684407, 684419, 684427, 684433, 684443, 684451, 684469, 684473, 684493, 684527, 684547, 684557, 684559, 684569, 684581, 684587, 684599, 684617, 684637, 684643, 684647, 684683, 684713, 684727, 684731, 684751, 684757, 684767, 684769, 684773, 684791, 684793, 684799, 684809, 684829, 684841, 684857, 684869, 684889, 684923, 684949, 684961, 684973, 684977, 684989, 685001, 685019, 685031, 685039, 685051, 685057, 685063, 685073, 685081, 685093, 685099, 685103, 685109, 685123, 685141, 685169, 685177, 685199, 685231, 685247, 685249, 685271, 685297, 685301, 685319, 685337, 685339, 685361, 685367, 685369, 685381, 685393, 685417, 685427, 685429, 685453, 685459, 685471, 685493, 685511, 685513, 685519, 685537, 685541, 685547, 685591, 685609, 685613, 685621, 685631, 685637, 685649, 685669, 685679, 685697, 685717, 685723, 685733, 685739, 685747, 685753, 685759, 685781, 685793, 685819, 685849, 685859, 685907, 685939, 685963, 685969, 685973, 685987, 685991, 686003, 686009, 686011, 686027, 686029, 686039, 686041, 686051, 686057, 686087, 686089, 686099, 686117, 686131, 686141, 686143, 686149, 686173, 686177, 686197, 686201, 686209, 686267, 686269, 686293, 686317, 686321, 686333, 686339, 686353, 686359, 686363, 686417, 686423, 686437, 686449, 686453, 686473, 686479, 686503, 686513, 686519, 686551, 686563, 686593, 686611, 686639, 686669, 686671, 686687, 686723, 686729, 686731, 686737, 686761, 686773, 686789, 686797, 686801, 686837, 686843, 686863, 686879, 686891, 686893, 686897, 686911, 686947, 686963, 686969, 686971, 686977, 686989, 686993, 687007, 687013, 687017, 687019, 687023, 687031, 687041, 687061, 687073, 687083, 687101, 687107, 687109, 687121, 687131, 687139, 687151, 687161, 687163, 687179, 687223, 687233, 687277, 687289, 687299, 687307, 687311, 687317, 687331, 687341, 687343, 687359, 687383, 687389, 687397, 687403, 687413, 687431, 687433, 687437, 687443, 687457, 687461, 687473, 687481, 687499, 687517, 687521, 687523, 687541, 687551, 687559, 687581, 687593, 687623, 687637, 687641, 687647, 687679, 687683, 687691, 687707, 687721, 687737, 687749, 687767, 687773, 687779, 687787, 687809, 687823, 687829, 687839, 687847, 687893, 687901, 687917, 687923, 687931, 687949, 687961, 687977, 688003, 688013, 688027, 688031, 688063, 688067, 688073, 688087, 688097, 688111, 688133, 688139, 688147, 688159, 688187, 688201, 688217, 688223, 688249, 688253, 688277, 688297, 688309, 688333, 688339, 688357, 688379, 688393, 688397, 688403, 688411, 688423, 688433, 688447, 688451, 688453, 688477, 688511, 688531, 688543, 688561, 688573, 688591, 688621, 688627, 688631, 688637, 688657, 688661, 688669, 688679, 688697, 688717, 688729, 688733, 688741, 688747, 688757, 688763, 688777, 688783, 688799, 688813, 688861, 688867, 688871, 688889, 688907, 688939, 688951, 688957, 688969, 688979, 688999, 689021, 689033, 689041, 689063, 689071, 689077, 689081, 689089, 689093, 689107, 689113, 689131, 689141, 689167, 689201, 689219, 689233, 689237, 689257, 689261, 689267, 689279, 689291, 689309, 689317, 689321, 689341, 689357, 689369, 689383, 689389, 689393, 689411, 689431, 689441, 689459, 689461, 689467, 689509, 689551, 689561, 689581, 689587, 689597, 689599, 689603, 689621, 689629, 689641, 689693, 689699, 689713, 689723, 689761, 689771, 689779, 689789, 689797, 689803, 689807, 689827, 689831, 689851, 689867, 689869, 689873, 689879, 689891, 689893, 689903, 689917, 689921, 689929, 689951, 689957, 689959, 689963, 689981, 689987, 690037, 690059, 690073, 690089, 690103, 690119, 690127, 690139, 690143, 690163, 690187, 690233, 690259, 690269, 690271, 690281, 690293, 690323, 690341, 690367, 690377, 690397, 690407, 690419, 690427, 690433, 690439, 690449, 690467, 690491, 690493, 690509, 690511, 690533, 690541, 690553, 690583, 690589, 690607, 690611, 690629, 690661, 690673, 690689, 690719, 690721, 690757, 690787, 690793, 690817, 690839, 690841, 690869, 690871, 690887, 690889, 690919, 690929, 690953, 690997, 691001, 691037, 691051, 691063, 691079, 691109, 691111, 691121, 691129, 691147, 691151, 691153, 691181, 691183, 691189, 691193, 691199, 691231, 691241, 691267, 691289, 691297, 691309, 691333, 691337, 691343, 691349, 691363, 691381, 691399, 691409, 691433, 691451, 691463, 691489, 691499, 691531, 691553, 691573, 691583, 691589, 691591, 691631, 691637, 691651, 691661, 691681, 691687, 691693, 691697, 691709, 691721, 691723, 691727, 691729, 691739, 691759, 691763, 691787, 691799, 691813, 691829, 691837, 691841, 691843, 691871, 691877, 691891, 691897, 691903, 691907, 691919, 691921, 691931, 691949, 691973, 691979, 691991, 691997, 692009, 692017, 692051, 692059, 692063, 692071, 692089, 692099, 692117, 692141, 692147, 692149, 692161, 692191, 692221, 692239, 692249, 692269, 692273, 692281, 692287, 692297, 692299, 692309, 692327, 692333, 692347, 692353, 692371, 692387, 692389, 692399, 692401, 692407, 692413, 692423, 692431, 692441, 692453, 692459, 692467, 692513, 692521, 692537, 692539, 692543, 692567, 692581, 692591, 692621, 692641, 692647, 692651, 692663, 692689, 692707, 692711, 692717, 692729, 692743, 692753, 692761, 692771, 692779, 692789, 692821, 692851, 692863, 692893, 692917, 692927, 692929, 692933, 692957, 692963, 692969, 692983, 693019, 693037, 693041, 693061, 693079, 693089, 693097, 693103, 693127, 693137, 693149, 693157, 693167, 693169, 693179, 693223, 693257, 693283, 693317, 693323, 693337, 693353, 693359, 693373, 693397, 693401, 693403, 693409, 693421, 693431, 693437, 693487, 693493, 693503, 693523, 693527, 693529, 693533, 693569, 693571, 693601, 693607, 693619, 693629, 693659, 693661, 693677, 693683, 693689, 693691, 693697, 693701, 693727, 693731, 693733, 693739, 693743, 693757, 693779, 693793, 693799, 693809, 693827, 693829, 693851, 693859, 693871, 693877, 693881, 693943, 693961, 693967, 693989, 694019, 694033, 694039, 694061, 694069, 694079, 694081, 694087, 694091, 694123, 694189, 694193, 694201, 694207, 694223, 694259, 694261, 694271, 694273, 694277, 694313, 694319, 694327, 694333, 694339, 694349, 694357, 694361, 694367, 694373, 694381, 694387, 694391, 694409, 694427, 694457, 694471, 694481, 694483, 694487, 694511, 694513, 694523, 694541, 694549, 694559, 694567, 694571, 694591, 694597, 694609, 694619, 694633, 694649, 694651, 694717, 694721, 694747, 694763, 694781, 694783, 694789, 694829, 694831, 694867, 694871, 694873, 694879, 694901, 694919, 694951, 694957, 694979, 694987, 694997, 694999, 695003, 695017, 695021, 695047, 695059, 695069, 695081, 695087, 695089, 695099, 695111, 695117, 695131, 695141, 695171, 695207, 695239, 695243, 695257, 695263, 695269, 695281, 695293, 695297, 695309, 695323, 695327, 695329, 695347, 695369, 695371, 695377, 695389, 695407, 695411, 695441, 695447, 695467, 695477, 695491, 695503, 695509, 695561, 695567, 695573, 695581, 695593, 695599, 695603, 695621, 695627, 695641, 695659, 695663, 695677, 695687, 695689, 695701, 695719, 695743, 695749, 695771, 695777, 695791, 695801, 695809, 695839, 695843, 695867, 695873, 695879, 695881, 695899, 695917, 695927, 695939, 695999, 696019, 696053, 696061, 696067, 696077, 696079, 696083, 696107, 696109, 696119, 696149, 696181, 696239, 696253, 696257, 696263, 696271, 696281, 696313, 696317, 696323, 696343, 696349, 696359, 696361, 696373, 696379, 696403, 696413, 696427, 696433, 696457, 696481, 696491, 696497, 696503, 696517, 696523, 696533, 696547, 696569, 696607, 696611, 696617, 696623, 696629, 696653, 696659, 696679, 696691, 696719, 696721, 696737, 696743, 696757, 696763, 696793, 696809, 696811, 696823, 696827, 696833, 696851, 696853, 696887, 696889, 696893, 696907, 696929, 696937, 696961, 696989, 696991, 697009, 697013, 697019, 697033, 697049, 697063, 697069, 697079, 697087, 697093, 697111, 697121, 697127, 697133, 697141, 697157, 697181, 697201, 697211, 697217, 697259, 697261, 697267, 697271, 697303, 697327, 697351, 697373, 697379, 697381, 697387, 697397, 697399, 697409, 697423, 697441, 697447, 697453, 697457, 697481, 697507, 697511, 697513, 697519, 697523, 697553, 697579, 697583, 697591, 697601, 697603, 697637, 697643, 697673, 697681, 697687, 697691, 697693, 697703, 697727, 697729, 697733, 697757, 697759, 697787, 697819, 697831, 697877, 697891, 697897, 697909, 697913, 697937, 697951, 697967, 697973, 697979, 697993, 697999, 698017, 698021, 698039, 698051, 698053, 698077, 698083, 698111, 698171, 698183, 698239, 698249, 698251, 698261, 698263, 698273, 698287, 698293, 698297, 698311, 698329, 698339, 698359, 698371, 698387, 698393, 698413, 698417, 698419, 698437, 698447, 698471, 698483, 698491, 698507, 698521, 698527, 698531, 698539, 698543, 698557, 698567, 698591, 698641, 698653, 698669, 698701, 698713, 698723, 698729, 698773, 698779, 698821, 698827, 698849, 698891, 698899, 698903, 698923, 698939, 698977, 698983, 699001, 699007, 699037, 699053, 699059, 699073, 699077, 699089, 699113, 699119, 699133, 699151, 699157, 699169, 699187, 699191, 699197, 699211, 699217, 699221, 699241, 699253, 699271, 699287, 699289, 699299, 699319, 699323, 699343, 699367, 699373, 699379, 699383, 699401, 699427, 699437, 699443, 699449, 699463, 699469, 699493, 699511, 699521, 699527, 699529, 699539, 699541, 699557, 699571, 699581, 699617, 699631, 699641, 699649, 699697, 699709, 699719, 699733, 699757, 699761, 699767, 699791, 699793, 699817, 699823, 699863, 699931, 699943, 699947, 699953, 699961, 699967};
		for(int i = 0,len=a.length;i<len;i++){
			prime.add(a[i]);
			primeMap.put(a[i], true);
		}
	}
	private static void init500000(){
		int[] a = new int[]{500009, 500029, 500041, 500057, 500069, 500083, 500107, 500111, 500113, 500119, 500153, 500167, 500173, 500177, 500179, 500197, 500209, 500231, 500233, 500237, 500239, 500249, 500257, 500287, 500299, 500317, 500321, 500333, 500341, 500363, 500369, 500389, 500393, 500413, 500417, 500431, 500443, 500459, 500471, 500473, 500483, 500501, 500509, 500519, 500527, 500567, 500579, 500587, 500603, 500629, 500671, 500677, 500693, 500699, 500713, 500719, 500723, 500729, 500741, 500777, 500791, 500807, 500809, 500831, 500839, 500861, 500873, 500881, 500887, 500891, 500909, 500911, 500921, 500923, 500933, 500947, 500953, 500957, 500977, 501001, 501013, 501019, 501029, 501031, 501037, 501043, 501077, 501089, 501103, 501121, 501131, 501133, 501139, 501157, 501173, 501187, 501191, 501197, 501203, 501209, 501217, 501223, 501229, 501233, 501257, 501271, 501287, 501299, 501317, 501341, 501343, 501367, 501383, 501401, 501409, 501419, 501427, 501451, 501463, 501493, 501503, 501511, 501563, 501577, 501593, 501601, 501617, 501623, 501637, 501659, 501691, 501701, 501703, 501707, 501719, 501731, 501769, 501779, 501803, 501817, 501821, 501827, 501829, 501841, 501863, 501889, 501911, 501931, 501947, 501953, 501967, 501971, 501997, 502001, 502013, 502039, 502043, 502057, 502063, 502079, 502081, 502087, 502093, 502121, 502133, 502141, 502171, 502181, 502217, 502237, 502247, 502259, 502261, 502277, 502301, 502321, 502339, 502393, 502409, 502421, 502429, 502441, 502451, 502487, 502499, 502501, 502507, 502517, 502543, 502549, 502553, 502591, 502597, 502613, 502631, 502633, 502643, 502651, 502669, 502687, 502699, 502703, 502717, 502729, 502769, 502771, 502781, 502787, 502807, 502819, 502829, 502841, 502847, 502861, 502883, 502919, 502921, 502937, 502961, 502973, 503003, 503017, 503039, 503053, 503077, 503123, 503131, 503137, 503147, 503159, 503197, 503207, 503213, 503227, 503231, 503233, 503249, 503267, 503287, 503297, 503303, 503317, 503339, 503351, 503359, 503369, 503381, 503383, 503389, 503407, 503413, 503423, 503431, 503441, 503453, 503483, 503501, 503543, 503549, 503551, 503563, 503593, 503599, 503609, 503611, 503621, 503623, 503647, 503653, 503663, 503707, 503717, 503743, 503753, 503771, 503777, 503779, 503791, 503803, 503819, 503821, 503827, 503851, 503857, 503869, 503879, 503911, 503927, 503929, 503939, 503947, 503959, 503963, 503969, 503983, 503989, 504001, 504011, 504017, 504047, 504061, 504073, 504103, 504121, 504139, 504143, 504149, 504151, 504157, 504181, 504187, 504197, 504209, 504221, 504247, 504269, 504289, 504299, 504307, 504311, 504323, 504337, 504349, 504353, 504359, 504377, 504379, 504389, 504403, 504457, 504461, 504473, 504479, 504521, 504523, 504527, 504547, 504563, 504593, 504599, 504607, 504617, 504619, 504631, 504661, 504667, 504671, 504677, 504683, 504727, 504767, 504787, 504797, 504799, 504817, 504821, 504851, 504853, 504857, 504871, 504877, 504893, 504901, 504929, 504937, 504943, 504947, 504953, 504967, 504983, 504989, 504991, 505027, 505031, 505033, 505049, 505051, 505061, 505067, 505073, 505091, 505097, 505111, 505117, 505123, 505129, 505139, 505157, 505159, 505181, 505187, 505201, 505213, 505231, 505237, 505277, 505279, 505283, 505301, 505313, 505319, 505321, 505327, 505339, 505357, 505367, 505369, 505399, 505409, 505411, 505429, 505447, 505459, 505469, 505481, 505493, 505501, 505511, 505513, 505523, 505537, 505559, 505573, 505601, 505607, 505613, 505619, 505633, 505639, 505643, 505657, 505663, 505669, 505691, 505693, 505709, 505711, 505727, 505759, 505763, 505777, 505781, 505811, 505819, 505823, 505867, 505871, 505877, 505907, 505919, 505927, 505949, 505961, 505969, 505979, 506047, 506071, 506083, 506101, 506113, 506119, 506131, 506147, 506171, 506173, 506183, 506201, 506213, 506251, 506263, 506269, 506281, 506291, 506327, 506329, 506333, 506339, 506347, 506351, 506357, 506381, 506393, 506417, 506423, 506449, 506459, 506461, 506479, 506491, 506501, 506507, 506531, 506533, 506537, 506551, 506563, 506573, 506591, 506593, 506599, 506609, 506629, 506647, 506663, 506683, 506687, 506689, 506699, 506729, 506731, 506743, 506773, 506783, 506791, 506797, 506809, 506837, 506843, 506861, 506873, 506887, 506893, 506899, 506903, 506911, 506929, 506941, 506963, 506983, 506993, 506999, 507029, 507049, 507071, 507077, 507079, 507103, 507109, 507113, 507119, 507137, 507139, 507149, 507151, 507163, 507193, 507197, 507217, 507289, 507301, 507313, 507317, 507329, 507347, 507349, 507359, 507361, 507371, 507383, 507401, 507421, 507431, 507461, 507491, 507497, 507499, 507503, 507523, 507557, 507571, 507589, 507593, 507599, 507607, 507631, 507641, 507667, 507673, 507691, 507697, 507713, 507719, 507743, 507757, 507779, 507781, 507797, 507803, 507809, 507821, 507827, 507839, 507883, 507901, 507907, 507917, 507919, 507937, 507953, 507961, 507971, 507979, 508009, 508019, 508021, 508033, 508037, 508073, 508087, 508091, 508097, 508103, 508129, 508159, 508171, 508187, 508213, 508223, 508229, 508237, 508243, 508259, 508271, 508273, 508297, 508301, 508327, 508331, 508349, 508363, 508367, 508373, 508393, 508433, 508439, 508451, 508471, 508477, 508489, 508499, 508513, 508517, 508531, 508549, 508559, 508567, 508577, 508579, 508583, 508619, 508621, 508637, 508643, 508661, 508693, 508709, 508727, 508771, 508789, 508799, 508811, 508817, 508841, 508847, 508867, 508901, 508903, 508909, 508913, 508919, 508931, 508943, 508951, 508957, 508961, 508969, 508973, 508987, 509023, 509027, 509053, 509063, 509071, 509087, 509101, 509123, 509137, 509147, 509149, 509203, 509221, 509227, 509239, 509263, 509281, 509287, 509293, 509297, 509317, 509329, 509359, 509363, 509389, 509393, 509413, 509417, 509429, 509441, 509449, 509477, 509513, 509521, 509543, 509549, 509557, 509563, 509569, 509573, 509581, 509591, 509603, 509623, 509633, 509647, 509653, 509659, 509681, 509687, 509689, 509693, 509699, 509723, 509731, 509737, 509741, 509767, 509783, 509797, 509801, 509833, 509837, 509843, 509863, 509867, 509879, 509909, 509911, 509921, 509939, 509947, 509959, 509963, 509989, 510007, 510031, 510047, 510049, 510061, 510067, 510073, 510077, 510079, 510089, 510101, 510121, 510127, 510137, 510157, 510179, 510199, 510203, 510217, 510227, 510233, 510241, 510247, 510253, 510271, 510287, 510299, 510311, 510319, 510331, 510361, 510379, 510383, 510401, 510403, 510449, 510451, 510457, 510463, 510481, 510529, 510551, 510553, 510569, 510581, 510583, 510589, 510611, 510613, 510617, 510619, 510677, 510683, 510691, 510707, 510709, 510751, 510767, 510773, 510793, 510803, 510817, 510823, 510827, 510847, 510889, 510907, 510919, 510931, 510941, 510943, 510989, 511001, 511013, 511019, 511033, 511039, 511057, 511061, 511087, 511109, 511111, 511123, 511151, 511153, 511163, 511169, 511171, 511177, 511193, 511201, 511211, 511213, 511223, 511237, 511243, 511261, 511279, 511289, 511297, 511327, 511333, 511337, 511351, 511361, 511387, 511391, 511409, 511417, 511439, 511447, 511453, 511457, 511463, 511477, 511487, 511507, 511519, 511523, 511541, 511549, 511559, 511573, 511579, 511583, 511591, 511603, 511627, 511631, 511633, 511669, 511691, 511703, 511711, 511723, 511757, 511787, 511793, 511801, 511811, 511831, 511843, 511859, 511867, 511873, 511891, 511897, 511909, 511933, 511939, 511961, 511963, 511991, 511997, 512009, 512011, 512021, 512047, 512059, 512093, 512101, 512137, 512147, 512167, 512207, 512249, 512251, 512269, 512287, 512311, 512321, 512333, 512353, 512389, 512419, 512429, 512443, 512467, 512497, 512503, 512507, 512521, 512531, 512537, 512543, 512569, 512573, 512579, 512581, 512591, 512593, 512597, 512609, 512621, 512641, 512657, 512663, 512671, 512683, 512711, 512713, 512717, 512741, 512747, 512761, 512767, 512779, 512797, 512803, 512819, 512821, 512843, 512849, 512891, 512899, 512903, 512917, 512921, 512927, 512929, 512959, 512977, 512989, 512999, 513001, 513013, 513017, 513031, 513041, 513047, 513053, 513059, 513067, 513083, 513101, 513103, 513109, 513131, 513137, 513157, 513167, 513169, 513173, 513203, 513239, 513257, 513269, 513277, 513283, 513307, 513311, 513313, 513319, 513341, 513347, 513353, 513367, 513371, 513397, 513407, 513419, 513427, 513431, 513439, 513473, 513479, 513481, 513509, 513511, 513529, 513533, 513593, 513631, 513641, 513649, 513673, 513679, 513683, 513691, 513697, 513719, 513727, 513731, 513739, 513749, 513761, 513767, 513769, 513781, 513829, 513839, 513841, 513871, 513881, 513899, 513917, 513923, 513937, 513943, 513977, 513991, 514001, 514009, 514013, 514021, 514049, 514051, 514057, 514061, 514079, 514081, 514093, 514103, 514117, 514123, 514127, 514147, 514177, 514187, 514201, 514219, 514229, 514243, 514247, 514249, 514271, 514277, 514289, 514309, 514313, 514333, 514343, 514357, 514361, 514379, 514399, 514417, 514429, 514433, 514453, 514499, 514513, 514519, 514523, 514529, 514531, 514543, 514561, 514571, 514621, 514637, 514639, 514643, 514649, 514651, 514669, 514681, 514711, 514733, 514739, 514741, 514747, 514751, 514757, 514769, 514783, 514793, 514819, 514823, 514831, 514841, 514847, 514853, 514859, 514867, 514873, 514889, 514903, 514933, 514939, 514949, 514967, 515041, 515087, 515089, 515111, 515143, 515149, 515153, 515173, 515191, 515227, 515231, 515233, 515237, 515279, 515293, 515311, 515323, 515351, 515357, 515369, 515371, 515377, 515381, 515401, 515429, 515477, 515507, 515519, 515539, 515563, 515579, 515587, 515597, 515611, 515621, 515639, 515651, 515653, 515663, 515677, 515681, 515687, 515693, 515701, 515737, 515741, 515761, 515771, 515773, 515777, 515783, 515803, 515813, 515839, 515843, 515857, 515861, 515873, 515887, 515917, 515923, 515929, 515941, 515951, 515969, 515993, 516017, 516023, 516049, 516053, 516077, 516091, 516127, 516151, 516157, 516161, 516163, 516169, 516179, 516193, 516199, 516209, 516223, 516227, 516233, 516247, 516251, 516253, 516277, 516283, 516293, 516319, 516323, 516349, 516359, 516361, 516371, 516377, 516391, 516407, 516421, 516431, 516433, 516437, 516449, 516457, 516469, 516493, 516499, 516517, 516521, 516539, 516541, 516563, 516587, 516589, 516599, 516611, 516617, 516619, 516623, 516643, 516653, 516673, 516679, 516689, 516701, 516709, 516713, 516721, 516727, 516757, 516793, 516811, 516821, 516829, 516839, 516847, 516871, 516877, 516883, 516907, 516911, 516931, 516947, 516949, 516959, 516973, 516977, 516979, 516991, 517003, 517043, 517061, 517067, 517073, 517079, 517081, 517087, 517091, 517129, 517151, 517169, 517177, 517183, 517189, 517207, 517211, 517217, 517229, 517241, 517243, 517249, 517261, 517267, 517277, 517289, 517303, 517337, 517343, 517367, 517373, 517381, 517393, 517399, 517403, 517411, 517417, 517457, 517459, 517469, 517471, 517481, 517487, 517499, 517501, 517507, 517511, 517513, 517547, 517549, 517553, 517571, 517577, 517589, 517597, 517603, 517609, 517613, 517619, 517637, 517639, 517711, 517717, 517721, 517729, 517733, 517739, 517747, 517817, 517823, 517831, 517861, 517873, 517877, 517901, 517919, 517927, 517931, 517949, 517967, 517981, 517991, 517999, 518017, 518047, 518057, 518059, 518083, 518099, 518101, 518113, 518123, 518129, 518131, 518137, 518153, 518159, 518171, 518179, 518191, 518207, 518209, 518233, 518237, 518239, 518249, 518261, 518291, 518299, 518311, 518327, 518341, 518387, 518389, 518411, 518417, 518429, 518431, 518447, 518467, 518471, 518473, 518509, 518521, 518533, 518543, 518579, 518587, 518597, 518611, 518621, 518657, 518689, 518699, 518717, 518729, 518737, 518741, 518743, 518747, 518759, 518761, 518767, 518779, 518801, 518803, 518807, 518809, 518813, 518831, 518863, 518867, 518893, 518911, 518933, 518953, 518981, 518983, 518989, 519011, 519031, 519037, 519067, 519083, 519089, 519091, 519097, 519107, 519119, 519121, 519131, 519151, 519161, 519193, 519217, 519227, 519229, 519247, 519257, 519269, 519283, 519287, 519301, 519307, 519349, 519353, 519359, 519371, 519373, 519383, 519391, 519413, 519427, 519433, 519457, 519487, 519499, 519509, 519521, 519523, 519527, 519539, 519551, 519553, 519577, 519581, 519587, 519611, 519619, 519643, 519647, 519667, 519683, 519691, 519703, 519713, 519733, 519737, 519769, 519787, 519793, 519797, 519803, 519817, 519863, 519881, 519889, 519907, 519917, 519919, 519923, 519931, 519943, 519947, 519971, 519989, 519997, 520019, 520021, 520031, 520043, 520063, 520067, 520073, 520103, 520111, 520123, 520129, 520151, 520193, 520213, 520241, 520279, 520291, 520297, 520307, 520309, 520313, 520339, 520349, 520357, 520361, 520363, 520369, 520379, 520381, 520393, 520409, 520411, 520423, 520427, 520433, 520447, 520451, 520529, 520547, 520549, 520567, 520571, 520589, 520607, 520609, 520621, 520631, 520633, 520649, 520679, 520691, 520699, 520703, 520717, 520721, 520747, 520759, 520763, 520787, 520813, 520837, 520841, 520853, 520867, 520889, 520913, 520921, 520943, 520957, 520963, 520967, 520969, 520981, 521009, 521021, 521023, 521039, 521041, 521047, 521051, 521063, 521107, 521119, 521137, 521153, 521161, 521167, 521173, 521177, 521179, 521201, 521231, 521243, 521251, 521267, 521281, 521299, 521309, 521317, 521329, 521357, 521359, 521363, 521369, 521377, 521393, 521399, 521401, 521429, 521447, 521471, 521483, 521491, 521497, 521503, 521519, 521527, 521533, 521537, 521539, 521551, 521557, 521567, 521581, 521603, 521641, 521657, 521659, 521669, 521671, 521693, 521707, 521723, 521743, 521749, 521753, 521767, 521777, 521789, 521791, 521809, 521813, 521819, 521831, 521861, 521869, 521879, 521881, 521887, 521897, 521903, 521923, 521929, 521981, 521993, 521999, 522017, 522037, 522047, 522059, 522061, 522073, 522079, 522083, 522113, 522127, 522157, 522161, 522167, 522191, 522199, 522211, 522227, 522229, 522233, 522239, 522251, 522259, 522281, 522283, 522289, 522317, 522323, 522337, 522371, 522373, 522383, 522391, 522409, 522413, 522439, 522449, 522469, 522479, 522497, 522517, 522521, 522523, 522541, 522553, 522569, 522601, 522623, 522637, 522659, 522661, 522673, 522677, 522679, 522689, 522703, 522707, 522719, 522737, 522749, 522757, 522761, 522763, 522787, 522811, 522827, 522829, 522839, 522853, 522857, 522871, 522881, 522883, 522887, 522919, 522943, 522947, 522959, 522961, 522989, 523007, 523021, 523031, 523049, 523093, 523097, 523109, 523129, 523169, 523177, 523207, 523213, 523219, 523261, 523297, 523307, 523333, 523349, 523351, 523357, 523387, 523403, 523417, 523427, 523433, 523459, 523463, 523487, 523489, 523493, 523511, 523519, 523541, 523543, 523553, 523571, 523573, 523577, 523597, 523603, 523631, 523637, 523639, 523657, 523667, 523669, 523673, 523681, 523717, 523729, 523741, 523759, 523763, 523771, 523777, 523793, 523801, 523829, 523847, 523867, 523877, 523903, 523907, 523927, 523937, 523949, 523969, 523987, 523997, 524047, 524053, 524057, 524063, 524071, 524081, 524087, 524099, 524113, 524119, 524123, 524149, 524171, 524189, 524197, 524201, 524203, 524219, 524221, 524231, 524243, 524257, 524261, 524269, 524287, 524309, 524341, 524347, 524351, 524353, 524369, 524387, 524389, 524411, 524413, 524429, 524453, 524497, 524507, 524509, 524519, 524521, 524591, 524593, 524599, 524633, 524669, 524681, 524683, 524701, 524707, 524731, 524743, 524789, 524801, 524803, 524827, 524831, 524857, 524863, 524869, 524873, 524893, 524899, 524921, 524933, 524939, 524941, 524947, 524957, 524959, 524963, 524969, 524971, 524981, 524983, 524999, 525001, 525013, 525017, 525029, 525043, 525101, 525127, 525137, 525143, 525157, 525163, 525167, 525191, 525193, 525199, 525209, 525221, 525241, 525247, 525253, 525257, 525299, 525313, 525353, 525359, 525361, 525373, 525377, 525379, 525391, 525397, 525409, 525431, 525433, 525439, 525457, 525461, 525467, 525491, 525493, 525517, 525529, 525533, 525541, 525571, 525583, 525593, 525599, 525607, 525641, 525649, 525671, 525677, 525697, 525709, 525713, 525719, 525727, 525731, 525739, 525769, 525773, 525781, 525809, 525817, 525839, 525869, 525871, 525887, 525893, 525913, 525923, 525937, 525947, 525949, 525953, 525961, 525979, 525983, 526027, 526037, 526049, 526051, 526063, 526067, 526069, 526073, 526087, 526117, 526121, 526139, 526157, 526159, 526189, 526193, 526199, 526213, 526223, 526231, 526249, 526271, 526283, 526289, 526291, 526297, 526307, 526367, 526373, 526381, 526387, 526391, 526397, 526423, 526429, 526441, 526453, 526459, 526483, 526499, 526501, 526511, 526531, 526543, 526571, 526573, 526583, 526601, 526619, 526627, 526633, 526637, 526649, 526651, 526657, 526667, 526679, 526681, 526703, 526709, 526717, 526733, 526739, 526741, 526759, 526763, 526777, 526781, 526829, 526831, 526837, 526853, 526859, 526871, 526909, 526913, 526931, 526937, 526943, 526951, 526957, 526963, 526993, 526997, 527053, 527057, 527063, 527069, 527071, 527081, 527099, 527123, 527129, 527143, 527159, 527161, 527173, 527179, 527203, 527207, 527209, 527237, 527251, 527273, 527281, 527291, 527327, 527333, 527347, 527353, 527377, 527381, 527393, 527399, 527407, 527411, 527419, 527441, 527447, 527453, 527489, 527507, 527533, 527557, 527563, 527581, 527591, 527599, 527603, 527623, 527627, 527633, 527671, 527699, 527701, 527729, 527741, 527749, 527753, 527789, 527803, 527809, 527819, 527843, 527851, 527869, 527881, 527897, 527909, 527921, 527929, 527941, 527981, 527983, 527987, 527993, 528001, 528013, 528041, 528043, 528053, 528091, 528097, 528107, 528127, 528131, 528137, 528163, 528167, 528191, 528197, 528217, 528223, 528247, 528263, 528289, 528299, 528313, 528317, 528329, 528373, 528383, 528391, 528401, 528403, 528413, 528419, 528433, 528469, 528487, 528491, 528509, 528511, 528527, 528559, 528611, 528623, 528629, 528631, 528659, 528667, 528673, 528679, 528691, 528707, 528709, 528719, 528763, 528779, 528791, 528799, 528811, 528821, 528823, 528833, 528863, 528877, 528881, 528883, 528911, 528929, 528947, 528967, 528971, 528973, 528991, 529003, 529007, 529027, 529033, 529037, 529043, 529049, 529051, 529097, 529103, 529117, 529121, 529127, 529129, 529153, 529157, 529181, 529183, 529213, 529229, 529237, 529241, 529259, 529271, 529273, 529301, 529307, 529313, 529327, 529343, 529349, 529357, 529381, 529393, 529411, 529421, 529423, 529471, 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580997, 581029, 581041, 581047, 581069, 581071, 581089, 581099, 581101, 581137, 581143, 581149, 581171, 581173, 581177, 581183, 581197, 581201, 581227, 581237, 581239, 581261, 581263, 581293, 581303, 581311, 581323, 581333, 581341, 581351, 581353, 581369, 581377, 581393, 581407, 581411, 581429, 581443, 581447, 581459, 581473, 581491, 581521, 581527, 581549, 581551, 581557, 581573, 581597, 581599, 581617, 581639, 581657, 581663, 581683, 581687, 581699, 581701, 581729, 581731, 581743, 581753, 581767, 581773, 581797, 581809, 581821, 581843, 581857, 581863, 581869, 581873, 581891, 581909, 581921, 581941, 581947, 581953, 581981, 581983, 582011, 582013, 582017, 582031, 582037, 582067, 582083, 582119, 582137, 582139, 582157, 582161, 582167, 582173, 582181, 582203, 582209, 582221, 582223, 582227, 582247, 582251, 582299, 582317, 582319, 582371, 582391, 582409, 582419, 582427, 582433, 582451, 582457, 582469, 582499, 582509, 582511, 582541, 582551, 582563, 582587, 582601, 582623, 582643, 582649, 582677, 582689, 582691, 582719, 582721, 582727, 582731, 582737, 582761, 582763, 582767, 582773, 582781, 582793, 582809, 582821, 582851, 582853, 582859, 582887, 582899, 582931, 582937, 582949, 582961, 582971, 582973, 582983, 583007, 583013, 583019, 583021, 583031, 583069, 583087, 583127, 583139, 583147, 583153, 583169, 583171, 583181, 583189, 583207, 583213, 583229, 583237, 583249, 583267, 583273, 583279, 583291, 583301, 583337, 583339, 583351, 583367, 583391, 583397, 583403, 583409, 583417, 583421, 583447, 583459, 583469, 583481, 583493, 583501, 583511, 583519, 583523, 583537, 583543, 583577, 583603, 583613, 583619, 583621, 583631, 583651, 583657, 583669, 583673, 583697, 583727, 583733, 583753, 583769, 583777, 583783, 583789, 583801, 583841, 583853, 583859, 583861, 583873, 583879, 583903, 583909, 583937, 583969, 583981, 583991, 583997, 584011, 584027, 584033, 584053, 584057, 584063, 584081, 584099, 584141, 584153, 584167, 584183, 584203, 584249, 584261, 584279, 584281, 584303, 584347, 584357, 584359, 584377, 584387, 584393, 584399, 584411, 584417, 584429, 584447, 584471, 584473, 584509, 584531, 584557, 584561, 584587, 584593, 584599, 584603, 584609, 584621, 584627, 584659, 584663, 584677, 584693, 584699, 584707, 584713, 584719, 584723, 584737, 584767, 584777, 584789, 584791, 584809, 584849, 584863, 584869, 584873, 584879, 584897, 584911, 584917, 584923, 584951, 584963, 584971, 584981, 584993, 584999, 585019, 585023, 585031, 585037, 585041, 585043, 585049, 585061, 585071, 585073, 585077, 585107, 585113, 585119, 585131, 585149, 585163, 585199, 585217, 585251, 585269, 585271, 585283, 585289, 585313, 585317, 585337, 585341, 585367, 585383, 585391, 585413, 585437, 585443, 585461, 585467, 585493, 585503, 585517, 585547, 585551, 585569, 585577, 585581, 585587, 585593, 585601, 585619, 585643, 585653, 585671, 585677, 585691, 585721, 585727, 585733, 585737, 585743, 585749, 585757, 585779, 585791, 585799, 585839, 585841, 585847, 585853, 585857, 585863, 585877, 585881, 585883, 585889, 585899, 585911, 585913, 585917, 585919, 585953, 585989, 585997, 586009, 586037, 586051, 586057, 586067, 586073, 586087, 586111, 586121, 586123, 586129, 586139, 586147, 586153, 586189, 586213, 586237, 586273, 586277, 586291, 586301, 586309, 586319, 586349, 586361, 586363, 586367, 586387, 586403, 586429, 586433, 586457, 586459, 586463, 586471, 586493, 586499, 586501, 586541, 586543, 586567, 586571, 586577, 586589, 586601, 586603, 586609, 586627, 586631, 586633, 586667, 586679, 586693, 586711, 586723, 586741, 586769, 586787, 586793, 586801, 586811, 586813, 586819, 586837, 586841, 586849, 586871, 586897, 586903, 586909, 586919, 586921, 586933, 586939, 586951, 586961, 586973, 586979, 586981, 587017, 587021, 587033, 587051, 587053, 587057, 587063, 587087, 587101, 587107, 587117, 587123, 587131, 587137, 587143, 587149, 587173, 587179, 587189, 587201, 587219, 587263, 587267, 587269, 587281, 587287, 587297, 587303, 587341, 587371, 587381, 587387, 587413, 587417, 587429, 587437, 587441, 587459, 587467, 587473, 587497, 587513, 587519, 587527, 587533, 587539, 587549, 587551, 587563, 587579, 587599, 587603, 587617, 587621, 587623, 587633, 587659, 587669, 587677, 587687, 587693, 587711, 587731, 587737, 587747, 587749, 587753, 587771, 587773, 587789, 587813, 587827, 587833, 587849, 587863, 587887, 587891, 587897, 587927, 587933, 587947, 587959, 587969, 587971, 587987, 587989, 587999, 588011, 588019, 588037, 588043, 588061, 588073, 588079, 588083, 588097, 588113, 588121, 588131, 588151, 588167, 588169, 588173, 588191, 588199, 588229, 588239, 588241, 588257, 588277, 588293, 588311, 588347, 588359, 588361, 588383, 588389, 588397, 588403, 588433, 588437, 588463, 588481, 588493, 588503, 588509, 588517, 588521, 588529, 588569, 588571, 588619, 588631, 588641, 588647, 588649, 588667, 588673, 588683, 588703, 588733, 588737, 588743, 588767, 588773, 588779, 588811, 588827, 588839, 588871, 588877, 588881, 588893, 588911, 588937, 588941, 588947, 588949, 588953, 588977, 589021, 589027, 589049, 589063, 589109, 589111, 589123, 589139, 589159, 589163, 589181, 589187, 589189, 589207, 589213, 589219, 589231, 589241, 589243, 589273, 589289, 589291, 589297, 589327, 589331, 589349, 589357, 589387, 589409, 589439, 589451, 589453, 589471, 589481, 589493, 589507, 589529, 589531, 589579, 589583, 589591, 589601, 589607, 589609, 589639, 589643, 589681, 589711, 589717, 589751, 589753, 589759, 589763, 589783, 589793, 589807, 589811, 589829, 589847, 589859, 589861, 589873, 589877, 589903, 589921, 589933, 589993, 589997, 590021, 590027, 590033, 590041, 590071, 590077, 590099, 590119, 590123, 590129, 590131, 590137, 590141, 590153, 590171, 590201, 590207, 590243, 590251, 590263, 590267, 590269, 590279, 590309, 590321, 590323, 590327, 590357, 590363, 590377, 590383, 590389, 590399, 590407, 590431, 590437, 590489, 590537, 590543, 590567, 590573, 590593, 590599, 590609, 590627, 590641, 590647, 590657, 590659, 590669, 590713, 590717, 590719, 590741, 590753, 590771, 590797, 590809, 590813, 590819, 590833, 590839, 590867, 590899, 590921, 590923, 590929, 590959, 590963, 590983, 590987, 591023, 591053, 591061, 591067, 591079, 591089, 591091, 591113, 591127, 591131, 591137, 591161, 591163, 591181, 591193, 591233, 591259, 591271, 591287, 591289, 591301, 591317, 591319, 591341, 591377, 591391, 591403, 591407, 591421, 591431, 591443, 591457, 591469, 591499, 591509, 591523, 591553, 591559, 591581, 591599, 591601, 591611, 591623, 591649, 591653, 591659, 591673, 591691, 591709, 591739, 591743, 591749, 591751, 591757, 591779, 591791, 591827, 591841, 591847, 591863, 591881, 591887, 591893, 591901, 591937, 591959, 591973, 592019, 592027, 592049, 592057, 592061, 592073, 592087, 592099, 592121, 592129, 592133, 592139, 592157, 592199, 592217, 592219, 592223, 592237, 592261, 592289, 592303, 592307, 592309, 592321, 592337, 592343, 592351, 592357, 592367, 592369, 592387, 592391, 592393, 592429, 592451, 592453, 592463, 592469, 592483, 592489, 592507, 592517, 592531, 592547, 592561, 592577, 592589, 592597, 592601, 592609, 592621, 592639, 592643, 592649, 592661, 592663, 592681, 592693, 592723, 592727, 592741, 592747, 592759, 592763, 592793, 592843, 592849, 592853, 592861, 592873, 592877, 592897, 592903, 592919, 592931, 592939, 592967, 592973, 592987, 592993, 593003, 593029, 593041, 593051, 593059, 593071, 593081, 593083, 593111, 593119, 593141, 593143, 593149, 593171, 593179, 593183, 593207, 593209, 593213, 593227, 593231, 593233, 593251, 593261, 593273, 593291, 593293, 593297, 593321, 593323, 593353, 593381, 593387, 593399, 593401, 593407, 593429, 593447, 593449, 593473, 593479, 593491, 593497, 593501, 593507, 593513, 593519, 593531, 593539, 593573, 593587, 593597, 593603, 593627, 593629, 593633, 593641, 593647, 593651, 593689, 593707, 593711, 593767, 593777, 593783, 593839, 593851, 593863, 593869, 593899, 593903, 593933, 593951, 593969, 593977, 593987, 593993, 594023, 594037, 594047, 594091, 594103, 594107, 594119, 594137, 594151, 594157, 594161, 594163, 594179, 594193, 594203, 594211, 594227, 594241, 594271, 594281, 594283, 594287, 594299, 594311, 594313, 594329, 594359, 594367, 594379, 594397, 594401, 594403, 594421, 594427, 594449, 594457, 594467, 594469, 594499, 594511, 594521, 594523, 594533, 594551, 594563, 594569, 594571, 594577, 594617, 594637, 594641, 594653, 594667, 594679, 594697, 594709, 594721, 594739, 594749, 594751, 594773, 594793, 594821, 594823, 594827, 594829, 594857, 594889, 594899, 594911, 594917, 594929, 594931, 594953, 594959, 594961, 594977, 594989, 595003, 595037, 595039, 595043, 595057, 595069, 595073, 595081, 595087, 595093, 595097, 595117, 595123, 595129, 595139, 595141, 595157, 595159, 595181, 595183, 595201, 595207, 595229, 595247, 595253, 595261, 595267, 595271, 595277, 595291, 595303, 595313, 595319, 595333, 595339, 595351, 595363, 595373, 595379, 595381, 595411, 595451, 595453, 595481, 595513, 595519, 595523, 595547, 595549, 595571, 595577, 595579, 595613, 595627, 595687, 595703, 595709, 595711, 595717, 595733, 595741, 595801, 595807, 595817, 595843, 595873, 595877, 595927, 595939, 595943, 595949, 595951, 595957, 595961, 595963, 595967, 595981, 596009, 596021, 596027, 596047, 596053, 596059, 596069, 596081, 596083, 596093, 596117, 596119, 596143, 596147, 596159, 596179, 596209, 596227, 596231, 596243, 596251, 596257, 596261, 596273, 596279, 596291, 596293, 596317, 596341, 596363, 596369, 596399, 596419, 596423, 596461, 596489, 596503, 596507, 596537, 596569, 596573, 596579, 596587, 596593, 596599, 596611, 596623, 596633, 596653, 596663, 596669, 596671, 596693, 596707, 596737, 596741, 596749, 596767, 596779, 596789, 596803, 596821, 596831, 596839, 596851, 596857, 596861, 596863, 596879, 596899, 596917, 596927, 596929, 596933, 596941, 596963, 596977, 596983, 596987, 597031, 597049, 597053, 597059, 597073, 597127, 597131, 597133, 597137, 597169, 597209, 597221, 597239, 597253, 597263, 597269, 597271, 597301, 597307, 597349, 597353, 597361, 597367, 597383, 597391, 597403, 597407, 597409, 597419, 597433, 597437, 597451, 597473, 597497, 597521, 597523, 597539, 597551, 597559, 597577, 597581, 597589, 597593, 597599, 597613, 597637, 597643, 597659, 597671, 597673, 597677, 597679, 597689, 597697, 597757, 597761, 597767, 597769, 597781, 597803, 597823, 597827, 597833, 597853, 597859, 597869, 597889, 597899, 597901, 597923, 597929, 597967, 597997, 598007, 598049, 598051, 598057, 598079, 598093, 598099, 598123, 598127, 598141, 598151, 598159, 598163, 598187, 598189, 598193, 598219, 598229, 598261, 598303, 598307, 598333, 598363, 598369, 598379, 598387, 598399, 598421, 598427, 598439, 598447, 598457, 598463, 598487, 598489, 598501, 598537, 598541, 598571, 598613, 598643, 598649, 598651, 598657, 598669, 598681, 598687, 598691, 598711, 598721, 598727, 598729, 598777, 598783, 598789, 598799, 598817, 598841, 598853, 598867, 598877, 598883, 598891, 598903, 598931, 598933, 598963, 598967, 598973, 598981, 598987, 598999, 599003, 599009, 599021, 599023, 599069, 599087, 599117, 599143, 599147, 599149, 599153, 599191, 599213, 599231, 599243, 599251, 599273, 599281, 599303, 599309, 599321, 599341, 599353, 599359, 599371, 599383, 599387, 599399, 599407, 599413, 599419, 599429, 599477, 599479, 599491, 599513, 599519, 599537, 599551, 599561, 599591, 599597, 599603, 599611, 599623, 599629, 599657, 599663, 599681, 599693, 599699, 599701, 599713, 599719, 599741, 599759, 599779, 599783, 599803, 599831, 599843, 599857, 599869, 599891, 599899, 599927, 599933, 599939, 599941, 599959, 599983, 599993, 599999};
		for(int i = 0,len=a.length;i<len;i++){
			prime.add(a[i]);
			primeMap.put(a[i], true);
		}
	}
	
	private static void init400000(){
		int[] a = new int[]{400009, 400031, 400033, 400051, 400067, 400069, 400087, 400093, 400109, 400123, 400151, 400157, 400187, 400199, 400207, 400217, 400237, 400243, 400247, 400249, 400261, 400277, 400291, 400297, 400307, 400313, 400321, 400331, 400339, 400381, 400391, 400409, 400417, 400429, 400441, 400457, 400471, 400481, 400523, 400559, 400579, 400597, 400601, 400607, 400619, 400643, 400651, 400657, 400679, 400681, 400703, 400711, 400721, 400723, 400739, 400753, 400759, 400823, 400837, 400849, 400853, 400859, 400871, 400903, 400927, 400931, 400943, 400949, 400963, 400997, 401017, 401029, 401039, 401053, 401057, 401069, 401077, 401087, 401101, 401113, 401119, 401161, 401173, 401179, 401201, 401209, 401231, 401237, 401243, 401279, 401287, 401309, 401311, 401321, 401329, 401341, 401347, 401371, 401381, 401393, 401407, 401411, 401417, 401473, 401477, 401507, 401519, 401537, 401539, 401551, 401567, 401587, 401593, 401627, 401629, 401651, 401669, 401671, 401689, 401707, 401711, 401743, 401771, 401773, 401809, 401813, 401827, 401839, 401861, 401867, 401887, 401903, 401909, 401917, 401939, 401953, 401957, 401959, 401981, 401987, 401993, 402023, 402029, 402037, 402043, 402049, 402053, 402071, 402089, 402091, 402107, 402131, 402133, 402137, 402139, 402197, 402221, 402223, 402239, 402253, 402263, 402277, 402299, 402307, 402313, 402329, 402331, 402341, 402343, 402359, 402361, 402371, 402379, 402383, 402403, 402419, 402443, 402487, 402503, 402511, 402517, 402527, 402529, 402541, 402551, 402559, 402581, 402583, 402587, 402593, 402601, 402613, 402631, 402691, 402697, 402739, 402751, 402757, 402761, 402763, 402767, 402769, 402797, 402803, 402817, 402823, 402847, 402851, 402859, 402863, 402869, 402881, 402923, 402943, 402947, 402949, 402991, 403001, 403003, 403037, 403043, 403049, 403057, 403061, 403063, 403079, 403097, 403103, 403133, 403141, 403159, 403163, 403181, 403219, 403241, 403243, 403253, 403261, 403267, 403289, 403301, 403309, 403327, 403331, 403339, 403363, 403369, 403387, 403391, 403433, 403439, 403483, 403499, 403511, 403537, 403547, 403549, 403553, 403567, 403577, 403591, 403603, 403607, 403621, 403649, 403661, 403679, 403681, 403687, 403703, 403717, 403721, 403729, 403757, 403783, 403787, 403817, 403829, 403831, 403849, 403861, 403867, 403877, 403889, 403901, 403933, 403951, 403957, 403969, 403979, 403981, 403993, 404009, 404011, 404017, 404021, 404029, 404051, 404081, 404099, 404113, 404119, 404123, 404161, 404167, 404177, 404189, 404191, 404197, 404213, 404221, 404249, 404251, 404267, 404269, 404273, 404291, 404309, 404321, 404323, 404357, 404381, 404387, 404389, 404399, 404419, 404423, 404429, 404431, 404449, 404461, 404483, 404489, 404497, 404507, 404513, 404527, 404531, 404533, 404539, 404557, 404597, 404671, 404693, 404699, 404713, 404773, 404779, 404783, 404819, 404827, 404837, 404843, 404849, 404851, 404941, 404951, 404959, 404969, 404977, 404981, 404983, 405001, 405011, 405029, 405037, 405047, 405049, 405071, 405073, 405089, 405091, 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479701, 479749, 479753, 479761, 479771, 479777, 479783, 479797, 479813, 479821, 479833, 479839, 479861, 479879, 479881, 479891, 479903, 479909, 479939, 479951, 479953, 479957, 479971, 480013, 480017, 480019, 480023, 480043, 480047, 480049, 480059, 480061, 480071, 480091, 480101, 480107, 480113, 480133, 480143, 480157, 480167, 480169, 480203, 480209, 480287, 480299, 480317, 480329, 480341, 480343, 480349, 480367, 480373, 480379, 480383, 480391, 480409, 480419, 480427, 480449, 480451, 480461, 480463, 480499, 480503, 480509, 480517, 480521, 480527, 480533, 480541, 480553, 480563, 480569, 480583, 480587, 480647, 480661, 480707, 480713, 480731, 480737, 480749, 480761, 480773, 480787, 480803, 480827, 480839, 480853, 480881, 480911, 480919, 480929, 480937, 480941, 480959, 480967, 480979, 480989, 481001, 481003, 481009, 481021, 481043, 481051, 481067, 481073, 481087, 481093, 481097, 481109, 481123, 481133, 481141, 481147, 481153, 481157, 481171, 481177, 481181, 481199, 481207, 481211, 481231, 481249, 481297, 481301, 481303, 481307, 481343, 481363, 481373, 481379, 481387, 481409, 481417, 481433, 481447, 481469, 481489, 481501, 481513, 481531, 481549, 481571, 481577, 481589, 481619, 481633, 481639, 481651, 481667, 481673, 481681, 481693, 481697, 481699, 481721, 481751, 481753, 481769, 481787, 481801, 481807, 481813, 481837, 481843, 481847, 481849, 481861, 481867, 481879, 481883, 481909, 481939, 481963, 481997, 482017, 482021, 482029, 482033, 482039, 482051, 482071, 482093, 482099, 482101, 482117, 482123, 482179, 482189, 482203, 482213, 482227, 482231, 482233, 482243, 482263, 482281, 482309, 482323, 482347, 482351, 482359, 482371, 482387, 482393, 482399, 482401, 482407, 482413, 482423, 482437, 482441, 482483, 482501, 482507, 482509, 482513, 482519, 482527, 482539, 482569, 482593, 482597, 482621, 482627, 482633, 482641, 482659, 482663, 482683, 482687, 482689, 482707, 482711, 482717, 482719, 482731, 482743, 482753, 482759, 482767, 482773, 482789, 482803, 482819, 482827, 482837, 482861, 482863, 482873, 482897, 482899, 482917, 482941, 482947, 482957, 482971, 483017, 483031, 483061, 483071, 483097, 483127, 483139, 483163, 483167, 483179, 483209, 483211, 483221, 483229, 483233, 483239, 483247, 483251, 483281, 483289, 483317, 483323, 483337, 483347, 483367, 483377, 483389, 483397, 483407, 483409, 483433, 483443, 483467, 483481, 483491, 483499, 483503, 483523, 483541, 483551, 483557, 483563, 483577, 483611, 483619, 483629, 483643, 483649, 483671, 483697, 483709, 483719, 483727, 483733, 483751, 483757, 483761, 483767, 483773, 483787, 483809, 483811, 483827, 483829, 483839, 483853, 483863, 483869, 483883, 483907, 483929, 483937, 483953, 483971, 483991, 484019, 484027, 484037, 484061, 484067, 484079, 484091, 484111, 484117, 484123, 484129, 484151, 484153, 484171, 484181, 484193, 484201, 484207, 484229, 484243, 484259, 484283, 484301, 484303, 484327, 484339, 484361, 484369, 484373, 484397, 484411, 484417, 484439, 484447, 484457, 484459, 484487, 484489, 484493, 484531, 484543, 484577, 484597, 484607, 484609, 484613, 484621, 484639, 484643, 484691, 484703, 484727, 484733, 484751, 484763, 484769, 484777, 484787, 484829, 484853, 484867, 484927, 484951, 484987, 484999, 485021, 485029, 485041, 485053, 485059, 485063, 485081, 485101, 485113, 485123, 485131, 485137, 485161, 485167, 485171, 485201, 485207, 485209, 485263, 485311, 485347, 485351, 485363, 485371, 485383, 485389, 485411, 485417, 485423, 485437, 485447, 485479, 485497, 485509, 485519, 485543, 485567, 485587, 485593, 485603, 485609, 485647, 485657, 485671, 485689, 485701, 485717, 485729, 485731, 485753, 485777, 485819, 485827, 485831, 485833, 485893, 485899, 485909, 485923, 485941, 485959, 485977, 485993, 486023, 486037, 486041, 486043, 486053, 486061, 486071, 486091, 486103, 486119, 486133, 486139, 486163, 486179, 486181, 486193, 486203, 486221, 486223, 486247, 486281, 486293, 486307, 486313, 486323, 486329, 486331, 486341, 486349, 486377, 486379, 486389, 486391, 486397, 486407, 486433, 486443, 486449, 486481, 486491, 486503, 486509, 486511, 486527, 486539, 486559, 486569, 486583, 486589, 486601, 486617, 486637, 486641, 486643, 486653, 486667, 486671, 486677, 486679, 486683, 486697, 486713, 486721, 486757, 486767, 486769, 486781, 486797, 486817, 486821, 486833, 486839, 486869, 486907, 486923, 486929, 486943, 486947, 486949, 486971, 486977, 486991, 487007, 487013, 487021, 487049, 487051, 487057, 487073, 487079, 487093, 487099, 487111, 487133, 487177, 487183, 487187, 487211, 487213, 487219, 487247, 487261, 487283, 487303, 487307, 487313, 487349, 487363, 487381, 487387, 487391, 487397, 487423, 487427, 487429, 487447, 487457, 487463, 487469, 487471, 487477, 487481, 487489, 487507, 487561, 487589, 487601, 487603, 487607, 487637, 487649, 487651, 487657, 487681, 487691, 487703, 487709, 487717, 487727, 487733, 487741, 487757, 487769, 487783, 487789, 487793, 487811, 487819, 487829, 487831, 487843, 487873, 487889, 487891, 487897, 487933, 487943, 487973, 487979, 487997, 488003, 488009, 488011, 488021, 488051, 488057, 488069, 488119, 488143, 488149, 488153, 488161, 488171, 488197, 488203, 488207, 488209, 488227, 488231, 488233, 488239, 488249, 488261, 488263, 488287, 488303, 488309, 488311, 488317, 488321, 488329, 488333, 488339, 488347, 488353, 488381, 488399, 488401, 488407, 488417, 488419, 488441, 488459, 488473, 488503, 488513, 488539, 488567, 488573, 488603, 488611, 488617, 488627, 488633, 488639, 488641, 488651, 488687, 488689, 488701, 488711, 488717, 488723, 488729, 488743, 488749, 488759, 488779, 488791, 488797, 488821, 488827, 488833, 488861, 488879, 488893, 488897, 488909, 488921, 488947, 488959, 488981, 488993, 489001, 489011, 489019, 489043, 489053, 489061, 489101, 489109, 489113, 489127, 489133, 489157, 489161, 489179, 489191, 489197, 489217, 489239, 489241, 489257, 489263, 489283, 489299, 489329, 489337, 489343, 489361, 489367, 489389, 489407, 489409, 489427, 489431, 489439, 489449, 489457, 489479, 489487, 489493, 489529, 489539, 489551, 489553, 489557, 489571, 489613, 489631, 489653, 489659, 489673, 489677, 489679, 489689, 489691, 489733, 489743, 489761, 489791, 489793, 489799, 489803, 489817, 489823, 489833, 489847, 489851, 489869, 489871, 489887, 489901, 489911, 489913, 489941, 489943, 489959, 489961, 489977, 489989, 490001, 490003, 490019, 490031, 490033, 490057, 490097, 490103, 490111, 490117, 490121, 490151, 490159, 490169, 490183, 490201, 490207, 490223, 490241, 490247, 490249, 490267, 490271, 490277, 490283, 490309, 490313, 490339, 490367, 490393, 490417, 490421, 490453, 490459, 490463, 490481, 490493, 490499, 490519, 490537, 490541, 490543, 490549, 490559, 490571, 490573, 490577, 490579, 490591, 490619, 490627, 490631, 490643, 490661, 490663, 490697, 490733, 490741, 490769, 490771, 490783, 490829, 490837, 490849, 490859, 490877, 490891, 490913, 490921, 490927, 490937, 490949, 490951, 490957, 490967, 490969, 490991, 490993, 491003, 491039, 491041, 491059, 491081, 491083, 491129, 491137, 491149, 491159, 491167, 491171, 491201, 491213, 491219, 491251, 491261, 491273, 491279, 491297, 491299, 491327, 491329, 491333, 491339, 491341, 491353, 491357, 491371, 491377, 491417, 491423, 491429, 491461, 491483, 491489, 491497, 491501, 491503, 491527, 491531, 491537, 491539, 491581, 491591, 491593, 491611, 491627, 491633, 491639, 491651, 491653, 491669, 491677, 491707, 491719, 491731, 491737, 491747, 491773, 491783, 491789, 491797, 491819, 491833, 491837, 491851, 491857, 491867, 491873, 491899, 491923, 491951, 491969, 491977, 491983, 492007, 492013, 492017, 492029, 492047, 492053, 492059, 492061, 492067, 492077, 492083, 492103, 492113, 492227, 492251, 492253, 492257, 492281, 492293, 492299, 492319, 492377, 492389, 492397, 492403, 492409, 492413, 492421, 492431, 492463, 492467, 492487, 492491, 492511, 492523, 492551, 492563, 492587, 492601, 492617, 492619, 492629, 492631, 492641, 492647, 492659, 492671, 492673, 492707, 492719, 492721, 492731, 492757, 492761, 492763, 492769, 492781, 492799, 492839, 492853, 492871, 492883, 492893, 492901, 492911, 492967, 492979, 493001, 493013, 493021, 493027, 493043, 493049, 493067, 493093, 493109, 493111, 493121, 493123, 493127, 493133, 493139, 493147, 493159, 493169, 493177, 493193, 493201, 493211, 493217, 493219, 493231, 493243, 493249, 493277, 493279, 493291, 493301, 493313, 493333, 493351, 493369, 493393, 493397, 493399, 493403, 493433, 493447, 493457, 493463, 493481, 493523, 493531, 493541, 493567, 493573, 493579, 493583, 493607, 493621, 493627, 493643, 493657, 493693, 493709, 493711, 493721, 493729, 493733, 493747, 493777, 493793, 493807, 493811, 493813, 493817, 493853, 493859, 493873, 493877, 493897, 493919, 493931, 493937, 493939, 493967, 493973, 493979, 493993, 494023, 494029, 494041, 494051, 494069, 494077, 494083, 494093, 494101, 494107, 494129, 494141, 494147, 494167, 494191, 494213, 494237, 494251, 494257, 494267, 494269, 494281, 494287, 494317, 494327, 494341, 494353, 494359, 494369, 494381, 494383, 494387, 494407, 494413, 494441, 494443, 494471, 494497, 494519, 494521, 494539, 494561, 494563, 494567, 494587, 494591, 494609, 494617, 494621, 494639, 494647, 494651, 494671, 494677, 494687, 494693, 494699, 494713, 494719, 494723, 494731, 494737, 494743, 494749, 494759, 494761, 494783, 494789, 494803, 494843, 494849, 494873, 494899, 494903, 494917, 494927, 494933, 494939, 494959, 494987, 495017, 495037, 495041, 495043, 495067, 495071, 495109, 495113, 495119, 495133, 495139, 495149, 495151, 495161, 495181, 495199, 495211, 495221, 495241, 495269, 495277, 495289, 495301, 495307, 495323, 495337, 495343, 495347, 495359, 495361, 495371, 495377, 495389, 495401, 495413, 495421, 495433, 495437, 495449, 495457, 495461, 495491, 495511, 495527, 495557, 495559, 495563, 495569, 495571, 495587, 495589, 495611, 495613, 495617, 495619, 495629, 495637, 495647, 495667, 495679, 495701, 495707, 495713, 495749, 495751, 495757, 495769, 495773, 495787, 495791, 495797, 495799, 495821, 495827, 495829, 495851, 495877, 495893, 495899, 495923, 495931, 495947, 495953, 495959, 495967, 495973, 495983, 496007, 496019, 496039, 496051, 496063, 496073, 496079, 496123, 496127, 496163, 496187, 496193, 496211, 496229, 496231, 496259, 496283, 496289, 496291, 496297, 496303, 496313, 496333, 496339, 496343, 496381, 496399, 496427, 496439, 496453, 496459, 496471, 496477, 496481, 496487, 496493, 496499, 496511, 496549, 496579, 496583, 496609, 496631, 496669, 496681, 496687, 496703, 496711, 496733, 496747, 496763, 496789, 496813, 496817, 496841, 496849, 496871, 496877, 496889, 496891, 496897, 496901, 496913, 496919, 496949, 496963, 496997, 496999, 497011, 497017, 497041, 497047, 497051, 497069, 497093, 497111, 497113, 497117, 497137, 497141, 497153, 497171, 497177, 497197, 497239, 497257, 497261, 497269, 497279, 497281, 497291, 497297, 497303, 497309, 497323, 497339, 497351, 497389, 497411, 497417, 497423, 497449, 497461, 497473, 497479, 497491, 497501, 497507, 497509, 497521, 497537, 497551, 497557, 497561, 497579, 497587, 497597, 497603, 497633, 497659, 497663, 497671, 497677, 497689, 497701, 497711, 497719, 497729, 497737, 497741, 497771, 497773, 497801, 497813, 497831, 497839, 497851, 497867, 497869, 497873, 497899, 497929, 497957, 497963, 497969, 497977, 497989, 497993, 497999, 498013, 498053, 498061, 498073, 498089, 498101, 498103, 498119, 498143, 498163, 498167, 498181, 498209, 498227, 498257, 498259, 498271, 498301, 498331, 498343, 498361, 498367, 498391, 498397, 498401, 498403, 498409, 498439, 498461, 498467, 498469, 498493, 498497, 498521, 498523, 498527, 498551, 498557, 498577, 498583, 498599, 498611, 498613, 498643, 498647, 498653, 498679, 498689, 498691, 498733, 498739, 498749, 498761, 498767, 498779, 498781, 498787, 498791, 498803, 498833, 498857, 498859, 498881, 498907, 498923, 498931, 498937, 498947, 498961, 498973, 498977, 498989, 499021, 499027, 499033, 499039, 499063, 499067, 499099, 499117, 499127, 499129, 499133, 499139, 499141, 499151, 499157, 499159, 499181, 499183, 499189, 499211, 499229, 499253, 499267, 499277, 499283, 499309, 499321, 499327, 499349, 499361, 499363, 499391, 499397, 499403, 499423, 499439, 499459, 499481, 499483, 499493, 499507, 499519, 499523, 499549, 499559, 499571, 499591, 499601, 499607, 499621, 499633, 499637, 499649, 499661, 499663, 499669, 499673, 499679, 499687, 499691, 499693, 499711, 499717, 499729, 499739, 499747, 499781, 499787, 499801, 499819, 499853, 499879, 499883, 499897, 499903, 499927, 499943, 499957, 499969, 499973, 499979};
		for(int i = 0,len=a.length;i<len;i++){
			prime.add(a[i]);
			primeMap.put(a[i], true);
		}
	}
	private static void init300000(){
		int[] a = new int[]{300007, 300017, 300023, 300043, 300073, 300089, 300109, 300119, 300137, 300149, 300151, 300163, 300187, 300191, 300193, 300221, 300229, 300233, 300239, 300247, 300277, 300299, 300301, 300317, 300319, 300323, 300331, 300343, 300347, 300367, 300397, 300413, 300427, 300431, 300439, 300463, 300481, 300491, 300493, 300497, 300499, 300511, 300557, 300569, 300581, 300583, 300589, 300593, 300623, 300631, 300647, 300649, 300661, 300667, 300673, 300683, 300691, 300719, 300721, 300733, 300739, 300743, 300749, 300757, 300761, 300779, 300787, 300799, 300809, 300821, 300823, 300851, 300857, 300869, 300877, 300889, 300893, 300929, 300931, 300953, 300961, 300967, 300973, 300977, 300997, 301013, 301027, 301039, 301051, 301057, 301073, 301079, 301123, 301127, 301141, 301153, 301159, 301177, 301181, 301183, 301211, 301219, 301237, 301241, 301243, 301247, 301267, 301303, 301319, 301331, 301333, 301349, 301361, 301363, 301381, 301403, 301409, 301423, 301429, 301447, 301459, 301463, 301471, 301487, 301489, 301493, 301501, 301531, 301577, 301579, 301583, 301591, 301601, 301619, 301627, 301643, 301649, 301657, 301669, 301673, 301681, 301703, 301711, 301747, 301751, 301753, 301759, 301789, 301793, 301813, 301831, 301841, 301843, 301867, 301877, 301897, 301901, 301907, 301913, 301927, 301933, 301943, 301949, 301979, 301991, 301993, 301997, 301999, 302009, 302053, 302111, 302123, 302143, 302167, 302171, 302173, 302189, 302191, 302213, 302221, 302227, 302261, 302273, 302279, 302287, 302297, 302299, 302317, 302329, 302399, 302411, 302417, 302429, 302443, 302459, 302483, 302507, 302513, 302551, 302563, 302567, 302573, 302579, 302581, 302587, 302593, 302597, 302609, 302629, 302647, 302663, 302681, 302711, 302723, 302747, 302759, 302767, 302779, 302791, 302801, 302831, 302833, 302837, 302843, 302851, 302857, 302873, 302891, 302903, 302909, 302921, 302927, 302941, 302959, 302969, 302971, 302977, 302983, 302989, 302999, 303007, 303011, 303013, 303019, 303029, 303049, 303053, 303073, 303089, 303091, 303097, 303119, 303139, 303143, 303151, 303157, 303187, 303217, 303257, 303271, 303283, 303287, 303293, 303299, 303307, 303313, 303323, 303337, 303341, 303361, 303367, 303371, 303377, 303379, 303389, 303409, 303421, 303431, 303463, 303469, 303473, 303491, 303493, 303497, 303529, 303539, 303547, 303551, 303553, 303571, 303581, 303587, 303593, 303613, 303617, 303619, 303643, 303647, 303649, 303679, 303683, 303689, 303691, 303703, 303713, 303727, 303731, 303749, 303767, 303781, 303803, 303817, 303827, 303839, 303859, 303871, 303889, 303907, 303917, 303931, 303937, 303959, 303983, 303997, 304009, 304013, 304021, 304033, 304039, 304049, 304063, 304067, 304069, 304081, 304091, 304099, 304127, 304151, 304153, 304163, 304169, 304193, 304211, 304217, 304223, 304253, 304259, 304279, 304301, 304303, 304331, 304349, 304357, 304363, 304373, 304391, 304393, 304411, 304417, 304429, 304433, 304439, 304457, 304459, 304477, 304481, 304489, 304501, 304511, 304517, 304523, 304537, 304541, 304553, 304559, 304561, 304597, 304609, 304631, 304643, 304651, 304663, 304687, 304709, 304723, 304729, 304739, 304751, 304757, 304763, 304771, 304781, 304789, 304807, 304813, 304831, 304847, 304849, 304867, 304879, 304883, 304897, 304901, 304903, 304907, 304933, 304937, 304943, 304949, 304961, 304979, 304981, 305017, 305021, 305023, 305029, 305033, 305047, 305069, 305093, 305101, 305111, 305113, 305119, 305131, 305143, 305147, 305209, 305219, 305231, 305237, 305243, 305267, 305281, 305297, 305329, 305339, 305351, 305353, 305363, 305369, 305377, 305401, 305407, 305411, 305413, 305419, 305423, 305441, 305449, 305471, 305477, 305479, 305483, 305489, 305497, 305521, 305533, 305551, 305563, 305581, 305593, 305597, 305603, 305611, 305621, 305633, 305639, 305663, 305717, 305719, 305741, 305743, 305749, 305759, 305761, 305771, 305783, 305803, 305821, 305839, 305849, 305857, 305861, 305867, 305873, 305917, 305927, 305933, 305947, 305971, 305999, 306011, 306023, 306029, 306041, 306049, 306083, 306091, 306121, 306133, 306139, 306149, 306157, 306167, 306169, 306191, 306193, 306209, 306239, 306247, 306253, 306259, 306263, 306301, 306329, 306331, 306347, 306349, 306359, 306367, 306377, 306389, 306407, 306419, 306421, 306431, 306437, 306457, 306463, 306473, 306479, 306491, 306503, 306511, 306517, 306529, 306533, 306541, 306563, 306577, 306587, 306589, 306643, 306653, 306661, 306689, 306701, 306703, 306707, 306727, 306739, 306749, 306763, 306781, 306809, 306821, 306827, 306829, 306847, 306853, 306857, 306871, 306877, 306883, 306893, 306899, 306913, 306919, 306941, 306947, 306949, 306953, 306991, 307009, 307019, 307031, 307033, 307067, 307079, 307091, 307093, 307103, 307121, 307129, 307147, 307163, 307169, 307171, 307187, 307189, 307201, 307243, 307253, 307259, 307261, 307267, 307273, 307277, 307283, 307289, 307301, 307337, 307339, 307361, 307367, 307381, 307397, 307399, 307409, 307423, 307451, 307471, 307481, 307511, 307523, 307529, 307537, 307543, 307577, 307583, 307589, 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380971, 380977, 380983, 381001, 381011, 381019, 381037, 381047, 381061, 381071, 381077, 381097, 381103, 381167, 381169, 381181, 381209, 381221, 381223, 381233, 381239, 381253, 381287, 381289, 381301, 381319, 381323, 381343, 381347, 381371, 381373, 381377, 381383, 381389, 381401, 381413, 381419, 381439, 381443, 381461, 381467, 381481, 381487, 381509, 381523, 381527, 381529, 381533, 381541, 381559, 381569, 381607, 381629, 381631, 381637, 381659, 381673, 381697, 381707, 381713, 381737, 381739, 381749, 381757, 381761, 381791, 381793, 381817, 381841, 381853, 381859, 381911, 381917, 381937, 381943, 381949, 381977, 381989, 381991, 382001, 382003, 382021, 382037, 382061, 382069, 382073, 382087, 382103, 382117, 382163, 382171, 382189, 382229, 382231, 382241, 382253, 382267, 382271, 382303, 382331, 382351, 382357, 382363, 382373, 382391, 382427, 382429, 382457, 382463, 382493, 382507, 382511, 382519, 382541, 382549, 382553, 382567, 382579, 382583, 382589, 382601, 382621, 382631, 382643, 382649, 382661, 382663, 382693, 382703, 382709, 382727, 382729, 382747, 382751, 382763, 382769, 382777, 382801, 382807, 382813, 382843, 382847, 382861, 382867, 382871, 382873, 382883, 382919, 382933, 382939, 382961, 382979, 382999, 383011, 383023, 383029, 383041, 383051, 383069, 383077, 383081, 383083, 383099, 383101, 383107, 383113, 383143, 383147, 383153, 383171, 383179, 383219, 383221, 383261, 383267, 383281, 383291, 383297, 383303, 383321, 383347, 383371, 383393, 383399, 383417, 383419, 383429, 383459, 383483, 383489, 383519, 383521, 383527, 383533, 383549, 383557, 383573, 383587, 383609, 383611, 383623, 383627, 383633, 383651, 383657, 383659, 383681, 383683, 383693, 383723, 383729, 383753, 383759, 383767, 383777, 383791, 383797, 383807, 383813, 383821, 383833, 383837, 383839, 383869, 383891, 383909, 383917, 383923, 383941, 383951, 383963, 383969, 383983, 383987, 384001, 384017, 384029, 384049, 384061, 384067, 384079, 384089, 384107, 384113, 384133, 384143, 384151, 384157, 384173, 384187, 384193, 384203, 384227, 384247, 384253, 384257, 384259, 384277, 384287, 384289, 384299, 384301, 384317, 384331, 384343, 384359, 384367, 384383, 384403, 384407, 384437, 384469, 384473, 384479, 384481, 384487, 384497, 384509, 384533, 384547, 384577, 384581, 384589, 384599, 384611, 384619, 384623, 384641, 384673, 384691, 384697, 384701, 384719, 384733, 384737, 384751, 384757, 384773, 384779, 384817, 384821, 384827, 384841, 384847, 384851, 384889, 384907, 384913, 384919, 384941, 384961, 384973, 385001, 385013, 385027, 385039, 385057, 385069, 385079, 385081, 385087, 385109, 385127, 385129, 385139, 385141, 385153, 385159, 385171, 385193, 385199, 385223, 385249, 385261, 385267, 385279, 385289, 385291, 385321, 385327, 385331, 385351, 385379, 385391, 385393, 385397, 385403, 385417, 385433, 385471, 385481, 385493, 385501, 385519, 385531, 385537, 385559, 385571, 385573, 385579, 385589, 385591, 385597, 385607, 385621, 385631, 385639, 385657, 385661, 385663, 385709, 385739, 385741, 385771, 385783, 385793, 385811, 385817, 385831, 385837, 385843, 385859, 385877, 385897, 385901, 385907, 385927, 385939, 385943, 385967, 385991, 385997, 386017, 386039, 386041, 386047, 386051, 386083, 386093, 386117, 386119, 386129, 386131, 386143, 386149, 386153, 386159, 386161, 386173, 386219, 386227, 386233, 386237, 386249, 386263, 386279, 386297, 386299, 386303, 386329, 386333, 386339, 386363, 386369, 386371, 386381, 386383, 386401, 386411, 386413, 386429, 386431, 386437, 386471, 386489, 386501, 386521, 386537, 386543, 386549, 386569, 386587, 386609, 386611, 386621, 386629, 386641, 386647, 386651, 386677, 386689, 386693, 386713, 386719, 386723, 386731, 386747, 386777, 386809, 386839, 386851, 386887, 386891, 386921, 386927, 386963, 386977, 386987, 386989, 386993, 387007, 387017, 387031, 387047, 387071, 387077, 387083, 387089, 387109, 387137, 387151, 387161, 387169, 387173, 387187, 387197, 387199, 387203, 387227, 387253, 387263, 387269, 387281, 387307, 387313, 387329, 387341, 387371, 387397, 387403, 387433, 387437, 387449, 387463, 387493, 387503, 387509, 387529, 387551, 387577, 387587, 387613, 387623, 387631, 387641, 387659, 387677, 387679, 387683, 387707, 387721, 387727, 387743, 387749, 387763, 387781, 387791, 387799, 387839, 387853, 387857, 387911, 387913, 387917, 387953, 387967, 387971, 387973, 387977, 388009, 388051, 388057, 388067, 388081, 388099, 388109, 388111, 388117, 388133, 388159, 388163, 388169, 388177, 388181, 388183, 388187, 388211, 388231, 388237, 388253, 388259, 388273, 388277, 388301, 388313, 388319, 388351, 388363, 388369, 388373, 388391, 388403, 388459, 388471, 388477, 388481, 388483, 388489, 388499, 388519, 388529, 388541, 388567, 388573, 388621, 388651, 388657, 388673, 388691, 388693, 388697, 388699, 388711, 388727, 388757, 388777, 388781, 388789, 388793, 388813, 388823, 388837, 388859, 388879, 388891, 388897, 388901, 388903, 388931, 388933, 388937, 388961, 388963, 388991, 389003, 389023, 389027, 389029, 389041, 389047, 389057, 389083, 389089, 389099, 389111, 389117, 389141, 389149, 389161, 389167, 389171, 389173, 389189, 389219, 389227, 389231, 389269, 389273, 389287, 389297, 389299, 389303, 389357, 389369, 389381, 389399, 389401, 389437, 389447, 389461, 389479, 389483, 389507, 389513, 389527, 389531, 389533, 389539, 389561, 389563, 389567, 389569, 389579, 389591, 389621, 389629, 389651, 389659, 389663, 389687, 389699, 389713, 389723, 389743, 389749, 389761, 389773, 389783, 389791, 389797, 389819, 389839, 389849, 389867, 389891, 389897, 389903, 389911, 389923, 389927, 389941, 389947, 389953, 389957, 389971, 389981, 389989, 389999, 390001, 390043, 390067, 390077, 390083, 390097, 390101, 390107, 390109, 390113, 390119, 390151, 390157, 390161, 390191, 390193, 390199, 390209, 390211, 390223, 390263, 390281, 390289, 390307, 390323, 390343, 390347, 390353, 390359, 390367, 390373, 390389, 390391, 390407, 390413, 390419, 390421, 390433, 390437, 390449, 390463, 390479, 390487, 390491, 390493, 390499, 390503, 390527, 390539, 390553, 390581, 390647, 390653, 390671, 390673, 390703, 390707, 390721, 390727, 390737, 390739, 390743, 390751, 390763, 390781, 390791, 390809, 390821, 390829, 390851, 390869, 390877, 390883, 390889, 390893, 390953, 390959, 390961, 390967, 390989, 390991, 391009, 391019, 391021, 391031, 391049, 391057, 391063, 391067, 391073, 391103, 391117, 391133, 391151, 391159, 391163, 391177, 391199, 391217, 391219, 391231, 391247, 391249, 391273, 391283, 391291, 391301, 391331, 391337, 391351, 391367, 391373, 391379, 391387, 391393, 391397, 391399, 391403, 391441, 391451, 391453, 391487, 391519, 391537, 391553, 391579, 391613, 391619, 391627, 391631, 391639, 391661, 391679, 391691, 391693, 391711, 391717, 391733, 391739, 391751, 391753, 391757, 391789, 391801, 391817, 391823, 391847, 391861, 391873, 391879, 391889, 391891, 391903, 391907, 391921, 391939, 391961, 391967, 391987, 391999, 392011, 392033, 392053, 392059, 392069, 392087, 392099, 392101, 392111, 392113, 392131, 392143, 392149, 392153, 392159, 392177, 392201, 392209, 392213, 392221, 392233, 392239, 392251, 392261, 392263, 392267, 392269, 392279, 392281, 392297, 392299, 392321, 392333, 392339, 392347, 392351, 392363, 392383, 392389, 392423, 392437, 392443, 392467, 392473, 392477, 392489, 392503, 392519, 392531, 392543, 392549, 392569, 392593, 392599, 392611, 392629, 392647, 392663, 392669, 392699, 392723, 392737, 392741, 392759, 392761, 392767, 392803, 392807, 392809, 392827, 392831, 392837, 392849, 392851, 392857, 392879, 392893, 392911, 392923, 392927, 392929, 392957, 392963, 392969, 392981, 392983, 393007, 393013, 393017, 393031, 393059, 393073, 393077, 393079, 393083, 393097, 393103, 393109, 393121, 393137, 393143, 393157, 393161, 393181, 393187, 393191, 393203, 393209, 393241, 393247, 393257, 393271, 393287, 393299, 393301, 393311, 393331, 393361, 393373, 393377, 393383, 393401, 393403, 393413, 393451, 393473, 393479, 393487, 393517, 393521, 393539, 393541, 393551, 393557, 393571, 393577, 393581, 393583, 393587, 393593, 393611, 393629, 393637, 393649, 393667, 393671, 393677, 393683, 393697, 393709, 393713, 393721, 393727, 393739, 393749, 393761, 393779, 393797, 393847, 393853, 393857, 393859, 393863, 393871, 393901, 393919, 393929, 393931, 393947, 393961, 393977, 393989, 393997, 394007, 394019, 394039, 394049, 394063, 394073, 394099, 394123, 394129, 394153, 394157, 394169, 394187, 394201, 394211, 394223, 394241, 394249, 394259, 394271, 394291, 394319, 394327, 394357, 394363, 394367, 394369, 394393, 394409, 394411, 394453, 394481, 394489, 394501, 394507, 394523, 394529, 394549, 394571, 394577, 394579, 394601, 394619, 394631, 394633, 394637, 394643, 394673, 394699, 394717, 394721, 394727, 394729, 394733, 394739, 394747, 394759, 394787, 394811, 394813, 394817, 394819, 394829, 394837, 394861, 394879, 394897, 394931, 394943, 394963, 394967, 394969, 394981, 394987, 394993, 395023, 395027, 395039, 395047, 395069, 395089, 395093, 395107, 395111, 395113, 395119, 395137, 395141, 395147, 395159, 395173, 395189, 395191, 395201, 395231, 395243, 395251, 395261, 395273, 395287, 395293, 395303, 395309, 395321, 395323, 395377, 395383, 395407, 395429, 395431, 395443, 395449, 395453, 395459, 395491, 395509, 395513, 395533, 395537, 395543, 395581, 395597, 395611, 395621, 395627, 395657, 395671, 395677, 395687, 395701, 395719, 395737, 395741, 395749, 395767, 395803, 395849, 395851, 395873, 395887, 395891, 395897, 395909, 395921, 395953, 395959, 395971, 396001, 396029, 396031, 396041, 396043, 396061, 396079, 396091, 396103, 396107, 396119, 396157, 396173, 396181, 396197, 396199, 396203, 396217, 396239, 396247, 396259, 396269, 396293, 396299, 396301, 396311, 396323, 396349, 396353, 396373, 396377, 396379, 396413, 396427, 396437, 396443, 396449, 396479, 396509, 396523, 396527, 396533, 396541, 396547, 396563, 396577, 396581, 396601, 396619, 396623, 396629, 396631, 396637, 396647, 396667, 396679, 396703, 396709, 396713, 396719, 396733, 396833, 396871, 396881, 396883, 396887, 396919, 396931, 396937, 396943, 396947, 396953, 396971, 396983, 396997, 397013, 397027, 397037, 397051, 397057, 397063, 397073, 397093, 397099, 397127, 397151, 397153, 397181, 397183, 397211, 397217, 397223, 397237, 397253, 397259, 397283, 397289, 397297, 397301, 397303, 397337, 397351, 397357, 397361, 397373, 397379, 397427, 397429, 397433, 397459, 397469, 397489, 397493, 397517, 397519, 397541, 397543, 397547, 397549, 397567, 397589, 397591, 397597, 397633, 397643, 397673, 397687, 397697, 397721, 397723, 397729, 397751, 397753, 397757, 397759, 397763, 397799, 397807, 397811, 397829, 397849, 397867, 397897, 397907, 397921, 397939, 397951, 397963, 397973, 397981, 398011, 398023, 398029, 398033, 398039, 398053, 398059, 398063, 398077, 398087, 398113, 398117, 398119, 398129, 398143, 398149, 398171, 398207, 398213, 398219, 398227, 398249, 398261, 398267, 398273, 398287, 398303, 398311, 398323, 398339, 398341, 398347, 398353, 398357, 398369, 398393, 398407, 398417, 398423, 398441, 398459, 398467, 398471, 398473, 398477, 398491, 398509, 398539, 398543, 398549, 398557, 398569, 398581, 398591, 398609, 398611, 398621, 398627, 398669, 398681, 398683, 398693, 398711, 398729, 398731, 398759, 398771, 398813, 398819, 398821, 398833, 398857, 398863, 398887, 398903, 398917, 398921, 398933, 398941, 398969, 398977, 398989, 399023, 399031, 399043, 399059, 399067, 399071, 399079, 399097, 399101, 399107, 399131, 399137, 399149, 399151, 399163, 399173, 399181, 399197, 399221, 399227, 399239, 399241, 399263, 399271, 399277, 399281, 399283, 399353, 399379, 399389, 399391, 399401, 399403, 399409, 399433, 399439, 399473, 399481, 399491, 399493, 399499, 399523, 399527, 399541, 399557, 399571, 399577, 399583, 399587, 399601, 399613, 399617, 399643, 399647, 399667, 399677, 399689, 399691, 399719, 399727, 399731, 399739, 399757, 399761, 399769, 399781, 399787, 399793, 399851, 399853, 399871, 399887, 399899, 399911, 399913, 399937, 399941, 399953, 399979, 399983, 399989};
		for(int i = 0,len=a.length;i<len;i++){
			prime.add(a[i]);
			primeMap.put(a[i], true);
		}
	}
	private static void init200000(){
		int[] a = new int[]{200003, 200009, 200017, 200023, 200029, 200033, 200041, 200063, 200087, 200117, 200131, 200153, 200159, 200171, 200177, 200183, 200191, 200201, 200227, 200231, 200237, 200257, 200273, 200293, 200297, 200323, 200329, 200341, 200351, 200357, 200363, 200371, 200381, 200383, 200401, 200407, 200437, 200443, 200461, 200467, 200483, 200513, 200569, 200573, 200579, 200587, 200591, 200597, 200609, 200639, 200657, 200671, 200689, 200699, 200713, 200723, 200731, 200771, 200779, 200789, 200797, 200807, 200843, 200861, 200867, 200869, 200881, 200891, 200899, 200903, 200909, 200927, 200929, 200971, 200983, 200987, 200989, 201007, 201011, 201031, 201037, 201049, 201073, 201101, 201107, 201119, 201121, 201139, 201151, 201163, 201167, 201193, 201203, 201209, 201211, 201233, 201247, 201251, 201281, 201287, 201307, 201329, 201337, 201359, 201389, 201401, 201403, 201413, 201437, 201449, 201451, 201473, 201491, 201493, 201497, 201499, 201511, 201517, 201547, 201557, 201577, 201581, 201589, 201599, 201611, 201623, 201629, 201653, 201661, 201667, 201673, 201683, 201701, 201709, 201731, 201743, 201757, 201767, 201769, 201781, 201787, 201791, 201797, 201809, 201821, 201823, 201827, 201829, 201833, 201847, 201881, 201889, 201893, 201907, 201911, 201919, 201923, 201937, 201947, 201953, 201961, 201973, 201979, 201997, 202001, 202021, 202031, 202049, 202061, 202063, 202067, 202087, 202099, 202109, 202121, 202127, 202129, 202183, 202187, 202201, 202219, 202231, 202243, 202277, 202289, 202291, 202309, 202327, 202339, 202343, 202357, 202361, 202381, 202387, 202393, 202403, 202409, 202441, 202471, 202481, 202493, 202519, 202529, 202549, 202567, 202577, 202591, 202613, 202621, 202627, 202637, 202639, 202661, 202667, 202679, 202693, 202717, 202729, 202733, 202747, 202751, 202753, 202757, 202777, 202799, 202817, 202823, 202841, 202859, 202877, 202879, 202889, 202907, 202921, 202931, 202933, 202949, 202967, 202973, 202981, 202987, 202999, 203011, 203017, 203023, 203039, 203051, 203057, 203117, 203141, 203173, 203183, 203207, 203209, 203213, 203221, 203227, 203233, 203249, 203279, 203293, 203309, 203311, 203317, 203321, 203323, 203339, 203341, 203351, 203353, 203363, 203381, 203383, 203387, 203393, 203417, 203419, 203429, 203431, 203449, 203459, 203461, 203531, 203549, 203563, 203569, 203579, 203591, 203617, 203627, 203641, 203653, 203657, 203659, 203663, 203669, 203713, 203761, 203767, 203771, 203773, 203789, 203807, 203809, 203821, 203843, 203857, 203869, 203873, 203897, 203909, 203911, 203921, 203947, 203953, 203969, 203971, 203977, 203989, 203999, 204007, 204013, 204019, 204023, 204047, 204059, 204067, 204101, 204107, 204133, 204137, 204143, 204151, 204161, 204163, 204173, 204233, 204251, 204299, 204301, 204311, 204319, 204329, 204331, 204353, 204359, 204361, 204367, 204371, 204377, 204397, 204427, 204431, 204437, 204439, 204443, 204461, 204481, 204487, 204509, 204511, 204517, 204521, 204557, 204563, 204583, 204587, 204599, 204601, 204613, 204623, 204641, 204667, 204679, 204707, 204719, 204733, 204749, 204751, 204781, 204791, 204793, 204797, 204803, 204821, 204857, 204859, 204871, 204887, 204913, 204917, 204923, 204931, 204947, 204973, 204979, 204983, 205019, 205031, 205033, 205043, 205063, 205069, 205081, 205097, 205103, 205111, 205129, 205133, 205141, 205151, 205157, 205171, 205187, 205201, 205211, 205213, 205223, 205237, 205253, 205267, 205297, 205307, 205319, 205327, 205339, 205357, 205391, 205397, 205399, 205417, 205421, 205423, 205427, 205433, 205441, 205453, 205463, 205477, 205483, 205487, 205493, 205507, 205519, 205529, 205537, 205549, 205553, 205559, 205589, 205603, 205607, 205619, 205627, 205633, 205651, 205657, 205661, 205663, 205703, 205721, 205759, 205763, 205783, 205817, 205823, 205837, 205847, 205879, 205883, 205913, 205937, 205949, 205951, 205957, 205963, 205967, 205981, 205991, 205993, 206009, 206021, 206027, 206033, 206039, 206047, 206051, 206069, 206077, 206081, 206083, 206123, 206153, 206177, 206179, 206183, 206191, 206197, 206203, 206209, 206221, 206233, 206237, 206249, 206251, 206263, 206273, 206279, 206281, 206291, 206299, 206303, 206341, 206347, 206351, 206369, 206383, 206399, 206407, 206411, 206413, 206419, 206447, 206461, 206467, 206477, 206483, 206489, 206501, 206519, 206527, 206543, 206551, 206593, 206597, 206603, 206623, 206627, 206639, 206641, 206651, 206699, 206749, 206779, 206783, 206803, 206807, 206813, 206819, 206821, 206827, 206879, 206887, 206897, 206909, 206911, 206917, 206923, 206933, 206939, 206951, 206953, 206993, 207013, 207017, 207029, 207037, 207041, 207061, 207073, 207079, 207113, 207121, 207127, 207139, 207169, 207187, 207191, 207197, 207199, 207227, 207239, 207241, 207257, 207269, 207287, 207293, 207301, 207307, 207329, 207331, 207341, 207343, 207367, 207371, 207377, 207401, 207409, 207433, 207443, 207457, 207463, 207469, 207479, 207481, 207491, 207497, 207509, 207511, 207517, 207521, 207523, 207541, 207547, 207551, 207563, 207569, 207589, 207593, 207619, 207629, 207643, 207653, 207661, 207671, 207673, 207679, 207709, 207719, 207721, 207743, 207763, 207769, 207797, 207799, 207811, 207821, 207833, 207847, 207869, 207877, 207923, 207931, 207941, 207947, 207953, 207967, 207971, 207973, 207997, 208001, 208003, 208009, 208037, 208049, 208057, 208067, 208073, 208099, 208111, 208121, 208129, 208139, 208141, 208147, 208189, 208207, 208213, 208217, 208223, 208231, 208253, 208261, 208277, 208279, 208283, 208291, 208309, 208319, 208333, 208337, 208367, 208379, 208387, 208391, 208393, 208409, 208433, 208441, 208457, 208459, 208463, 208469, 208489, 208493, 208499, 208501, 208511, 208513, 208519, 208529, 208553, 208577, 208589, 208591, 208609, 208627, 208631, 208657, 208667, 208673, 208687, 208697, 208699, 208721, 208729, 208739, 208759, 208787, 208799, 208807, 208837, 208843, 208877, 208889, 208891, 208907, 208927, 208931, 208933, 208961, 208963, 208991, 208993, 208997, 209021, 209029, 209039, 209063, 209071, 209089, 209123, 209147, 209159, 209173, 209179, 209189, 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280603, 280607, 280613, 280627, 280639, 280673, 280681, 280697, 280699, 280703, 280711, 280717, 280729, 280751, 280759, 280769, 280771, 280811, 280817, 280837, 280843, 280859, 280871, 280879, 280883, 280897, 280909, 280913, 280921, 280927, 280933, 280939, 280949, 280957, 280963, 280967, 280979, 280997, 281023, 281033, 281053, 281063, 281069, 281081, 281117, 281131, 281153, 281159, 281167, 281189, 281191, 281207, 281227, 281233, 281243, 281249, 281251, 281273, 281279, 281291, 281297, 281317, 281321, 281327, 281339, 281353, 281357, 281363, 281381, 281419, 281423, 281429, 281431, 281509, 281527, 281531, 281539, 281549, 281551, 281557, 281563, 281579, 281581, 281609, 281621, 281623, 281627, 281641, 281647, 281651, 281653, 281663, 281669, 281683, 281717, 281719, 281737, 281747, 281761, 281767, 281777, 281783, 281791, 281797, 281803, 281807, 281833, 281837, 281839, 281849, 281857, 281867, 281887, 281893, 281921, 281923, 281927, 281933, 281947, 281959, 281971, 281989, 281993, 282001, 282011, 282019, 282053, 282059, 282071, 282089, 282091, 282097, 282101, 282103, 282127, 282143, 282157, 282167, 282221, 282229, 282239, 282241, 282253, 282281, 282287, 282299, 282307, 282311, 282313, 282349, 282377, 282383, 282389, 282391, 282407, 282409, 282413, 282427, 282439, 282461, 282481, 282487, 282493, 282559, 282563, 282571, 282577, 282589, 282599, 282617, 282661, 282671, 282677, 282679, 282683, 282691, 282697, 282703, 282707, 282713, 282767, 282769, 282773, 282797, 282809, 282827, 282833, 282847, 282851, 282869, 282881, 282889, 282907, 282911, 282913, 282917, 282959, 282973, 282977, 282991, 283001, 283007, 283009, 283027, 283051, 283079, 283093, 283097, 283099, 283111, 283117, 283121, 283133, 283139, 283159, 283163, 283181, 283183, 283193, 283207, 283211, 283267, 283277, 283289, 283303, 283369, 283397, 283403, 283411, 283447, 283463, 283487, 283489, 283501, 283511, 283519, 283541, 283553, 283571, 283573, 283579, 283583, 283601, 283607, 283609, 283631, 283637, 283639, 283669, 283687, 283697, 283721, 283741, 283763, 283769, 283771, 283793, 283799, 283807, 283813, 283817, 283831, 283837, 283859, 283861, 283873, 283909, 283937, 283949, 283957, 283961, 283979, 284003, 284023, 284041, 284051, 284057, 284059, 284083, 284093, 284111, 284117, 284129, 284131, 284149, 284153, 284159, 284161, 284173, 284191, 284201, 284227, 284231, 284233, 284237, 284243, 284261, 284267, 284269, 284293, 284311, 284341, 284357, 284369, 284377, 284387, 284407, 284413, 284423, 284429, 284447, 284467, 284477, 284483, 284489, 284507, 284509, 284521, 284527, 284539, 284551, 284561, 284573, 284587, 284591, 284593, 284623, 284633, 284651, 284657, 284659, 284681, 284689, 284701, 284707, 284723, 284729, 284731, 284737, 284741, 284743, 284747, 284749, 284759, 284777, 284783, 284803, 284807, 284813, 284819, 284831, 284833, 284839, 284857, 284881, 284897, 284899, 284917, 284927, 284957, 284969, 284989, 285007, 285023, 285031, 285049, 285071, 285079, 285091, 285101, 285113, 285119, 285121, 285139, 285151, 285161, 285179, 285191, 285199, 285221, 285227, 285251, 285281, 285283, 285287, 285289, 285301, 285317, 285343, 285377, 285421, 285433, 285451, 285457, 285463, 285469, 285473, 285497, 285517, 285521, 285533, 285539, 285553, 285557, 285559, 285569, 285599, 285611, 285613, 285629, 285631, 285641, 285643, 285661, 285667, 285673, 285697, 285707, 285709, 285721, 285731, 285749, 285757, 285763, 285767, 285773, 285781, 285823, 285827, 285839, 285841, 285871, 285937, 285949, 285953, 285977, 285979, 285983, 285997, 286001, 286009, 286019, 286043, 286049, 286061, 286063, 286073, 286103, 286129, 286163, 286171, 286199, 286243, 286249, 286289, 286301, 286333, 286367, 286369, 286381, 286393, 286397, 286411, 286421, 286427, 286453, 286457, 286459, 286469, 286477, 286483, 286487, 286493, 286499, 286513, 286519, 286541, 286543, 286547, 286553, 286589, 286591, 286609, 286613, 286619, 286633, 286651, 286673, 286687, 286697, 286703, 286711, 286721, 286733, 286751, 286753, 286763, 286771, 286777, 286789, 286801, 286813, 286831, 286859, 286873, 286927, 286973, 286981, 286987, 286999, 287003, 287047, 287057, 287059, 287087, 287093, 287099, 287107, 287117, 287137, 287141, 287149, 287159, 287167, 287173, 287179, 287191, 287219, 287233, 287237, 287239, 287251, 287257, 287269, 287279, 287281, 287291, 287297, 287321, 287327, 287333, 287341, 287347, 287383, 287387, 287393, 287437, 287449, 287491, 287501, 287503, 287537, 287549, 287557, 287579, 287597, 287611, 287629, 287669, 287671, 287681, 287689, 287701, 287731, 287747, 287783, 287789, 287801, 287813, 287821, 287849, 287851, 287857, 287863, 287867, 287873, 287887, 287921, 287933, 287939, 287977, 288007, 288023, 288049, 288053, 288061, 288077, 288089, 288109, 288137, 288179, 288181, 288191, 288199, 288203, 288209, 288227, 288241, 288247, 288257, 288283, 288293, 288307, 288313, 288317, 288349, 288359, 288361, 288383, 288389, 288403, 288413, 288427, 288433, 288461, 288467, 288481, 288493, 288499, 288527, 288529, 288539, 288551, 288559, 288571, 288577, 288583, 288647, 288649, 288653, 288661, 288679, 288683, 288689, 288697, 288731, 288733, 288751, 288767, 288773, 288803, 288817, 288823, 288833, 288839, 288851, 288853, 288877, 288907, 288913, 288929, 288931, 288947, 288973, 288979, 288989, 288991, 288997, 289001, 289019, 289021, 289031, 289033, 289039, 289049, 289063, 289067, 289099, 289103, 289109, 289111, 289127, 289129, 289139, 289141, 289151, 289169, 289171, 289181, 289189, 289193, 289213, 289241, 289243, 289249, 289253, 289273, 289283, 289291, 289297, 289309, 289319, 289343, 289349, 289361, 289369, 289381, 289397, 289417, 289423, 289439, 289453, 289463, 289469, 289477, 289489, 289511, 289543, 289559, 289573, 289577, 289589, 289603, 289607, 289637, 289643, 289657, 289669, 289717, 289721, 289727, 289733, 289741, 289759, 289763, 289771, 289789, 289837, 289841, 289843, 289847, 289853, 289859, 289871, 289889, 289897, 289937, 289951, 289957, 289967, 289973, 289987, 289999, 290011, 290021, 290023, 290027, 290033, 290039, 290041, 290047, 290057, 290083, 290107, 290113, 290119, 290137, 290141, 290161, 290183, 290189, 290201, 290209, 290219, 290233, 290243, 290249, 290317, 290327, 290347, 290351, 290359, 290369, 290383, 290393, 290399, 290419, 290429, 290441, 290443, 290447, 290471, 290473, 290489, 290497, 290509, 290527, 290531, 290533, 290539, 290557, 290593, 290597, 290611, 290617, 290621, 290623, 290627, 290657, 290659, 290663, 290669, 290671, 290677, 290701, 290707, 290711, 290737, 290761, 290767, 290791, 290803, 290821, 290827, 290837, 290839, 290861, 290869, 290879, 290897, 290923, 290959, 290963, 290971, 290987, 290993, 290999, 291007, 291013, 291037, 291041, 291043, 291077, 291089, 291101, 291103, 291107, 291113, 291143, 291167, 291169, 291173, 291191, 291199, 291209, 291217, 291253, 291257, 291271, 291287, 291293, 291299, 291331, 291337, 291349, 291359, 291367, 291371, 291373, 291377, 291419, 291437, 291439, 291443, 291457, 291481, 291491, 291503, 291509, 291521, 291539, 291547, 291559, 291563, 291569, 291619, 291647, 291649, 291661, 291677, 291689, 291691, 291701, 291721, 291727, 291743, 291751, 291779, 291791, 291817, 291829, 291833, 291853, 291857, 291869, 291877, 291887, 291899, 291901, 291923, 291971, 291979, 291983, 291997, 292021, 292027, 292037, 292057, 292069, 292079, 292081, 292091, 292093, 292133, 292141, 292147, 292157, 292181, 292183, 292223, 292231, 292241, 292249, 292267, 292283, 292301, 292309, 292319, 292343, 292351, 292363, 292367, 292381, 292393, 292427, 292441, 292459, 292469, 292471, 292477, 292483, 292489, 292493, 292517, 292531, 292541, 292549, 292561, 292573, 292577, 292601, 292627, 292631, 292661, 292667, 292673, 292679, 292693, 292703, 292709, 292711, 292717, 292727, 292753, 292759, 292777, 292793, 292801, 292807, 292819, 292837, 292841, 292849, 292867, 292879, 292909, 292921, 292933, 292969, 292973, 292979, 292993, 293021, 293071, 293081, 293087, 293093, 293099, 293107, 293123, 293129, 293147, 293149, 293173, 293177, 293179, 293201, 293207, 293213, 293221, 293257, 293261, 293263, 293269, 293311, 293329, 293339, 293351, 293357, 293399, 293413, 293431, 293441, 293453, 293459, 293467, 293473, 293483, 293507, 293543, 293599, 293603, 293617, 293621, 293633, 293639, 293651, 293659, 293677, 293681, 293701, 293717, 293723, 293729, 293749, 293767, 293773, 293791, 293803, 293827, 293831, 293861, 293863, 293893, 293899, 293941, 293957, 293983, 293989, 293999, 294001, 294013, 294023, 294029, 294043, 294053, 294059, 294067, 294103, 294127, 294131, 294149, 294157, 294167, 294169, 294179, 294181, 294199, 294211, 294223, 294227, 294241, 294247, 294251, 294269, 294277, 294289, 294293, 294311, 294313, 294317, 294319, 294337, 294341, 294347, 294353, 294383, 294391, 294397, 294403, 294431, 294439, 294461, 294467, 294479, 294499, 294509, 294523, 294529, 294551, 294563, 294629, 294641, 294647, 294649, 294659, 294673, 294703, 294731, 294751, 294757, 294761, 294773, 294781, 294787, 294793, 294799, 294803, 294809, 294821, 294829, 294859, 294869, 294887, 294893, 294911, 294919, 294923, 294947, 294949, 294953, 294979, 294989, 294991, 294997, 295007, 295033, 295037, 295039, 295049, 295073, 295079, 295081, 295111, 295123, 295129, 295153, 295187, 295199, 295201, 295219, 295237, 295247, 295259, 295271, 295277, 295283, 295291, 295313, 295319, 295333, 295357, 295363, 295387, 295411, 295417, 295429, 295433, 295439, 295441, 295459, 295513, 295517, 295541, 295553, 295567, 295571, 295591, 295601, 295663, 295693, 295699, 295703, 295727, 295751, 295759, 295769, 295777, 295787, 295819, 295831, 295837, 295843, 295847, 295853, 295861, 295871, 295873, 295877, 295879, 295901, 295903, 295909, 295937, 295943, 295949, 295951, 295961, 295973, 295993, 296011, 296017, 296027, 296041, 296047, 296071, 296083, 296099, 296117, 296129, 296137, 296159, 296183, 296201, 296213, 296221, 296237, 296243, 296249, 296251, 296269, 296273, 296279, 296287, 296299, 296347, 296353, 296363, 296369, 296377, 296437, 296441, 296473, 296477, 296479, 296489, 296503, 296507, 296509, 296519, 296551, 296557, 296561, 296563, 296579, 296581, 296587, 296591, 296627, 296651, 296663, 296669, 296683, 296687, 296693, 296713, 296719, 296729, 296731, 296741, 296749, 296753, 296767, 296771, 296773, 296797, 296801, 296819, 296827, 296831, 296833, 296843, 296909, 296911, 296921, 296929, 296941, 296969, 296971, 296981, 296983, 296987, 297019, 297023, 297049, 297061, 297067, 297079, 297083, 297097, 297113, 297133, 297151, 297161, 297169, 297191, 297233, 297247, 297251, 297257, 297263, 297289, 297317, 297359, 297371, 297377, 297391, 297397, 297403, 297421, 297439, 297457, 297467, 297469, 297481, 297487, 297503, 297509, 297523, 297533, 297581, 297589, 297601, 297607, 297613, 297617, 297623, 297629, 297641, 297659, 297683, 297691, 297707, 297719, 297727, 297757, 297779, 297793, 297797, 297809, 297811, 297833, 297841, 297853, 297881, 297889, 297893, 297907, 297911, 297931, 297953, 297967, 297971, 297989, 297991, 298013, 298021, 298031, 298043, 298049, 298063, 298087, 298093, 298099, 298153, 298157, 298159, 298169, 298171, 298187, 298201, 298211, 298213, 298223, 298237, 298247, 298261, 298283, 298303, 298307, 298327, 298339, 298343, 298349, 298369, 298373, 298399, 298409, 298411, 298427, 298451, 298477, 298483, 298513, 298559, 298579, 298583, 298589, 298601, 298607, 298621, 298631, 298651, 298667, 298679, 298681, 298687, 298691, 298693, 298709, 298723, 298733, 298757, 298759, 298777, 298799, 298801, 298817, 298819, 298841, 298847, 298853, 298861, 298897, 298937, 298943, 298993, 298999, 299011, 299017, 299027, 299029, 299053, 299059, 299063, 299087, 299099, 299107, 299113, 299137, 299147, 299171, 299179, 299191, 299197, 299213, 299239, 299261, 299281, 299287, 299311, 299317, 299329, 299333, 299357, 299359, 299363, 299371, 299389, 299393, 299401, 299417, 299419, 299447, 299471, 299473, 299477, 299479, 299501, 299513, 299521, 299527, 299539, 299567, 299569, 299603, 299617, 299623, 299653, 299671, 299681, 299683, 299699, 299701, 299711, 299723, 299731, 299743, 299749, 299771, 299777, 299807, 299843, 299857, 299861, 299881, 299891, 299903, 299909, 299933, 299941, 299951, 299969, 299977, 299983, 299993};
		for(int i = 0,len=a.length;i<len;i++){
			prime.add(a[i]);
			primeMap.put(a[i], true);
		}
	}
	
	private static void init100500(){
		int[] a = new int[]{105019, 105023, 105031, 105037, 105071, 105097, 105107, 105137, 105143, 105167, 105173, 105199, 105211, 105227, 105229, 105239, 105251, 105253, 105263, 105269, 105277, 105319, 105323, 105331, 105337, 105341, 105359, 105361, 105367, 105373, 105379, 105389, 105397, 105401, 105407, 105437, 105449, 105467, 105491, 105499, 105503, 105509, 105517, 105527, 105529, 105533, 105541, 105557, 105563, 105601, 105607, 105613, 105619, 105649, 105653, 105667, 105673, 105683, 105691, 105701, 105727, 105733, 105751, 105761, 105767, 105769, 105817, 105829, 105863, 105871, 105883, 105899, 105907, 105913, 105929, 105943, 105953, 105967, 105971, 105977, 105983, 105997, 106013, 106019, 106031, 106033, 106087, 106103, 106109, 106121, 106123, 106129, 106163, 106181, 106187, 106189, 106207, 106213, 106217, 106219, 106243, 106261, 106273, 106277, 106279, 106291, 106297, 106303, 106307, 106319, 106321, 106331, 106349, 106357, 106363, 106367, 106373, 106391, 106397, 106411, 106417, 106427, 106433, 106441, 106451, 106453, 106487, 106501, 106531, 106537, 106541, 106543, 106591, 106619, 106621, 106627, 106637, 106649, 106657, 106661, 106663, 106669, 106681, 106693, 106699, 106703, 106721, 106727, 106739, 106747, 106751, 106753, 106759, 106781, 106783, 106787, 106801, 106823, 106853, 106859, 106861, 106867, 106871, 106877, 106903, 106907, 106921, 106937, 106949, 106957, 106961, 106963, 106979, 106993, 107021, 107033, 107053, 107057, 107069, 107071, 107077, 107089, 107099, 107101, 107119, 107123, 107137, 107171, 107183, 107197, 107201, 107209, 107227, 107243, 107251, 107269, 107273, 107279, 107309, 107323, 107339, 107347, 107351, 107357, 107377, 107441, 107449, 107453, 107467, 107473, 107507, 107509, 107563, 107581, 107599, 107603, 107609, 107621, 107641, 107647, 107671, 107687, 107693, 107699, 107713, 107717, 107719, 107741, 107747, 107761, 107773, 107777, 107791, 107827, 107837, 107839, 107843, 107857, 107867, 107873, 107881, 107897, 107903, 107923, 107927, 107941, 107951, 107971, 107981, 107999, 108007, 108011, 108013, 108023, 108037, 108041, 108061, 108079, 108089, 108107, 108109, 108127, 108131, 108139, 108161, 108179, 108187, 108191, 108193, 108203, 108211, 108217, 108223, 108233, 108247, 108263, 108271, 108287, 108289, 108293, 108301, 108343, 108347, 108359, 108377, 108379, 108401, 108413, 108421, 108439, 108457, 108461, 108463, 108497, 108499, 108503, 108517, 108529, 108533, 108541, 108553, 108557, 108571, 108587, 108631, 108637, 108643, 108649, 108677, 108707, 108709, 108727, 108739, 108751, 108761, 108769, 108791, 108793, 108799, 108803, 108821, 108827, 108863, 108869, 108877, 108881, 108883, 108887, 108893, 108907, 108917, 108923, 108929, 108943, 108947, 108949, 108959, 108961, 108967, 108971, 108991, 109001, 109013, 109037, 109049, 109063, 109073, 109097, 109103, 109111, 109121, 109133, 109139, 109141, 109147, 109159, 109169, 109171, 109199, 109201, 109211, 109229, 109253, 109267, 109279, 109297, 109303, 109313, 109321, 109331, 109357, 109363, 109367, 109379, 109387, 109391, 109397, 109423, 109433, 109441, 109451, 109453, 109469, 109471, 109481, 109507, 109517, 109519, 109537, 109541, 109547, 109567, 109579, 109583, 109589, 109597, 109609, 109619, 109621, 109639, 109661, 109663, 109673, 109717, 109721, 109741, 109751, 109789, 109793, 109807, 109819, 109829, 109831, 109841, 109843, 109847, 109849, 109859, 109873, 109883, 109891, 109897, 109903, 109913, 109919, 109937, 109943, 109961, 109987, 110017, 110023, 110039, 110051, 110059, 110063, 110069, 110083, 110119, 110129, 110161, 110183, 110221, 110233, 110237, 110251, 110261, 110269, 110273, 110281, 110291, 110311, 110321, 110323, 110339, 110359, 110419, 110431, 110437, 110441, 110459, 110477, 110479, 110491, 110501, 110503, 110527, 110533, 110543, 110557, 110563, 110567, 110569, 110573, 110581, 110587, 110597, 110603, 110609, 110623, 110629, 110641, 110647, 110651, 110681, 110711, 110729, 110731, 110749, 110753, 110771, 110777, 110807, 110813, 110819, 110821, 110849, 110863, 110879, 110881, 110899, 110909, 110917, 110921, 110923, 110927, 110933, 110939, 110947, 110951, 110969, 110977, 110989, 111029, 111031, 111043, 111049, 111053, 111091, 111103, 111109, 111119, 111121, 111127, 111143, 111149, 111187, 111191, 111211, 111217, 111227, 111229, 111253, 111263, 111269, 111271, 111301, 111317, 111323, 111337, 111341, 111347, 111373, 111409, 111427, 111431, 111439, 111443, 111467, 111487, 111491, 111493, 111497, 111509, 111521, 111533, 111539, 111577, 111581, 111593, 111599, 111611, 111623, 111637, 111641, 111653, 111659, 111667, 111697, 111721, 111731, 111733, 111751, 111767, 111773, 111779, 111781, 111791, 111799, 111821, 111827, 111829, 111833, 111847, 111857, 111863, 111869, 111871, 111893, 111913, 111919, 111949, 111953, 111959, 111973, 111977, 111997, 112019, 112031, 112061, 112067, 112069, 112087, 112097, 112103, 112111, 112121, 112129, 112139, 112153, 112163, 112181, 112199, 112207, 112213, 112223, 112237, 112241, 112247, 112249, 112253, 112261, 112279, 112289, 112291, 112297, 112303, 112327, 112331, 112337, 112339, 112349, 112361, 112363, 112397, 112403, 112429, 112459, 112481, 112501, 112507, 112543, 112559, 112571, 112573, 112577, 112583, 112589, 112601, 112603, 112621, 112643, 112657, 112663, 112687, 112691, 112741, 112757, 112759, 112771, 112787, 112799, 112807, 112831, 112843, 112859, 112877, 112901, 112909, 112913, 112919, 112921, 112927, 112939, 112951, 112967, 112979, 112997, 113011, 113017, 113021, 113023, 113027, 113039, 113041, 113051, 113063, 113081, 113083, 113089, 113093, 113111, 113117, 113123, 113131, 113143, 113147, 113149, 113153, 113159, 113161, 113167, 113171, 113173, 113177, 113189, 113209, 113213, 113227, 113233, 113279, 113287, 113327, 113329, 113341, 113357, 113359, 113363, 113371, 113381, 113383, 113417, 113437, 113453, 113467, 113489, 113497, 113501, 113513, 113537, 113539, 113557, 113567, 113591, 113621, 113623, 113647, 113657, 113683, 113717, 113719, 113723, 113731, 113749, 113759, 113761, 113777, 113779, 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186727, 186733, 186743, 186757, 186761, 186763, 186773, 186793, 186799, 186841, 186859, 186869, 186871, 186877, 186883, 186889, 186917, 186947, 186959, 187003, 187009, 187027, 187043, 187049, 187067, 187069, 187073, 187081, 187091, 187111, 187123, 187127, 187129, 187133, 187139, 187141, 187163, 187171, 187177, 187181, 187189, 187193, 187211, 187217, 187219, 187223, 187237, 187273, 187277, 187303, 187337, 187339, 187349, 187361, 187367, 187373, 187379, 187387, 187393, 187409, 187417, 187423, 187433, 187441, 187463, 187469, 187471, 187477, 187507, 187513, 187531, 187547, 187559, 187573, 187597, 187631, 187633, 187637, 187639, 187651, 187661, 187669, 187687, 187699, 187711, 187721, 187751, 187763, 187787, 187793, 187823, 187843, 187861, 187871, 187877, 187883, 187897, 187907, 187909, 187921, 187927, 187931, 187951, 187963, 187973, 187987, 188011, 188017, 188021, 188029, 188107, 188137, 188143, 188147, 188159, 188171, 188179, 188189, 188197, 188249, 188261, 188273, 188281, 188291, 188299, 188303, 188311, 188317, 188323, 188333, 188351, 188359, 188369, 188389, 188401, 188407, 188417, 188431, 188437, 188443, 188459, 188473, 188483, 188491, 188519, 188527, 188533, 188563, 188579, 188603, 188609, 188621, 188633, 188653, 188677, 188681, 188687, 188693, 188701, 188707, 188711, 188719, 188729, 188753, 188767, 188779, 188791, 188801, 188827, 188831, 188833, 188843, 188857, 188861, 188863, 188869, 188891, 188911, 188927, 188933, 188939, 188941, 188953, 188957, 188983, 188999, 189011, 189017, 189019, 189041, 189043, 189061, 189067, 189127, 189139, 189149, 189151, 189169, 189187, 189199, 189223, 189229, 189239, 189251, 189253, 189257, 189271, 189307, 189311, 189337, 189347, 189349, 189353, 189361, 189377, 189389, 189391, 189401, 189407, 189421, 189433, 189437, 189439, 189463, 189467, 189473, 189479, 189491, 189493, 189509, 189517, 189523, 189529, 189547, 189559, 189583, 189593, 189599, 189613, 189617, 189619, 189643, 189653, 189661, 189671, 189691, 189697, 189701, 189713, 189733, 189743, 189757, 189767, 189797, 189799, 189817, 189823, 189851, 189853, 189859, 189877, 189881, 189887, 189901, 189913, 189929, 189947, 189949, 189961, 189967, 189977, 189983, 189989, 189997, 190027, 190031, 190051, 190063, 190093, 190097, 190121, 190129, 190147, 190159, 190181, 190207, 190243, 190249, 190261, 190271, 190283, 190297, 190301, 190313, 190321, 190331, 190339, 190357, 190367, 190369, 190387, 190391, 190403, 190409, 190471, 190507, 190523, 190529, 190537, 190543, 190573, 190577, 190579, 190583, 190591, 190607, 190613, 190633, 190639, 190649, 190657, 190667, 190669, 190699, 190709, 190711, 190717, 190753, 190759, 190763, 190769, 190783, 190787, 190793, 190807, 190811, 190823, 190829, 190837, 190843, 190871, 190889, 190891, 190901, 190909, 190913, 190921, 190979, 190997, 191021, 191027, 191033, 191039, 191047, 191057, 191071, 191089, 191099, 191119, 191123, 191137, 191141, 191143, 191161, 191173, 191189, 191227, 191231, 191237, 191249, 191251, 191281, 191297, 191299, 191339, 191341, 191353, 191413, 191441, 191447, 191449, 191453, 191459, 191461, 191467, 191473, 191491, 191497, 191507, 191509, 191519, 191531, 191533, 191537, 191551, 191561, 191563, 191579, 191599, 191621, 191627, 191657, 191669, 191671, 191677, 191689, 191693, 191699, 191707, 191717, 191747, 191749, 191773, 191783, 191791, 191801, 191803, 191827, 191831, 191833, 191837, 191861, 191899, 191903, 191911, 191929, 191953, 191969, 191977, 191999, 192007, 192013, 192029, 192037, 192043, 192047, 192053, 192091, 192097, 192103, 192113, 192121, 192133, 192149, 192161, 192173, 192187, 192191, 192193, 192229, 192233, 192239, 192251, 192259, 192263, 192271, 192307, 192317, 192319, 192323, 192341, 192343, 192347, 192373, 192377, 192383, 192391, 192407, 192431, 192461, 192463, 192497, 192499, 192529, 192539, 192547, 192553, 192557, 192571, 192581, 192583, 192587, 192601, 192611, 192613, 192617, 192629, 192631, 192637, 192667, 192677, 192697, 192737, 192743, 192749, 192757, 192767, 192781, 192791, 192799, 192811, 192817, 192833, 192847, 192853, 192859, 192877, 192883, 192887, 192889, 192917, 192923, 192931, 192949, 192961, 192971, 192977, 192979, 192991, 193003, 193009, 193013, 193031, 193043, 193051, 193057, 193073, 193093, 193133, 193139, 193147, 193153, 193163, 193181, 193183, 193189, 193201, 193243, 193247, 193261, 193283, 193301, 193327, 193337, 193357, 193367, 193373, 193379, 193381, 193387, 193393, 193423, 193433, 193441, 193447, 193451, 193463, 193469, 193493, 193507, 193513, 193541, 193549, 193559, 193573, 193577, 193597, 193601, 193603, 193607, 193619, 193649, 193663, 193679, 193703, 193723, 193727, 193741, 193751, 193757, 193763, 193771, 193789, 193793, 193799, 193811, 193813, 193841, 193847, 193859, 193861, 193871, 193873, 193877, 193883, 193891, 193937, 193939, 193943, 193951, 193957, 193979, 193993, 194003, 194017, 194027, 194057, 194069, 194071, 194083, 194087, 194093, 194101, 194113, 194119, 194141, 194149, 194167, 194179, 194197, 194203, 194239, 194263, 194267, 194269, 194309, 194323, 194353, 194371, 194377, 194413, 194431, 194443, 194471, 194479, 194483, 194507, 194521, 194527, 194543, 194569, 194581, 194591, 194609, 194647, 194653, 194659, 194671, 194681, 194683, 194687, 194707, 194713, 194717, 194723, 194729, 194749, 194767, 194771, 194809, 194813, 194819, 194827, 194839, 194861, 194863, 194867, 194869, 194891, 194899, 194911, 194917, 194933, 194963, 194977, 194981, 194989, 195023, 195029, 195043, 195047, 195049, 195053, 195071, 195077, 195089, 195103, 195121, 195127, 195131, 195137, 195157, 195161, 195163, 195193, 195197, 195203, 195229, 195241, 195253, 195259, 195271, 195277, 195281, 195311, 195319, 195329, 195341, 195343, 195353, 195359, 195389, 195401, 195407, 195413, 195427, 195443, 195457, 195469, 195479, 195493, 195497, 195511, 195527, 195539, 195541, 195581, 195593, 195599, 195659, 195677, 195691, 195697, 195709, 195731, 195733, 195737, 195739, 195743, 195751, 195761, 195781, 195787, 195791, 195809, 195817, 195863, 195869, 195883, 195887, 195893, 195907, 195913, 195919, 195929, 195931, 195967, 195971, 195973, 195977, 195991, 195997, 196003, 196033, 196039, 196043, 196051, 196073, 196081, 196087, 196111, 196117, 196139, 196159, 196169, 196171, 196177, 196181, 196187, 196193, 196201, 196247, 196271, 196277, 196279, 196291, 196303, 196307, 196331, 196337, 196379, 196387, 196429, 196439, 196453, 196459, 196477, 196499, 196501, 196519, 196523, 196541, 196543, 196549, 196561, 196579, 196583, 196597, 196613, 196643, 196657, 196661, 196663, 196681, 196687, 196699, 196709, 196717, 196727, 196739, 196751, 196769, 196771, 196799, 196817, 196831, 196837, 196853, 196871, 196873, 196879, 196901, 196907, 196919, 196927, 196961, 196991, 196993, 197003, 197009, 197023, 197033, 197059, 197063, 197077, 197083, 197089, 197101, 197117, 197123, 197137, 197147, 197159, 197161, 197203, 197207, 197221, 197233, 197243, 197257, 197261, 197269, 197273, 197279, 197293, 197297, 197299, 197311, 197339, 197341, 197347, 197359, 197369, 197371, 197381, 197383, 197389, 197419, 197423, 197441, 197453, 197479, 197507, 197521, 197539, 197551, 197567, 197569, 197573, 197597, 197599, 197609, 197621, 197641, 197647, 197651, 197677, 197683, 197689, 197699, 197711, 197713, 197741, 197753, 197759, 197767, 197773, 197779, 197803, 197807, 197831, 197837, 197887, 197891, 197893, 197909, 197921, 197927, 197933, 197947, 197957, 197959, 197963, 197969, 197971, 198013, 198017, 198031, 198043, 198047, 198073, 198083, 198091, 198097, 198109, 198127, 198139, 198173, 198179, 198193, 198197, 198221, 198223, 198241, 198251, 198257, 198259, 198277, 198281, 198301, 198313, 198323, 198337, 198347, 198349, 198377, 198391, 198397, 198409, 198413, 198427, 198437, 198439, 198461, 198463, 198469, 198479, 198491, 198503, 198529, 198533, 198553, 198571, 198589, 198593, 198599, 198613, 198623, 198637, 198641, 198647, 198659, 198673, 198689, 198701, 198719, 198733, 198761, 198769, 198811, 198817, 198823, 198827, 198829, 198833, 198839, 198841, 198851, 198859, 198899, 198901, 198929, 198937, 198941, 198943, 198953, 198959, 198967, 198971, 198977, 198997, 199021, 199033, 199037, 199039, 199049, 199081, 199103, 199109, 199151, 199153, 199181, 199193, 199207, 199211, 199247, 199261, 199267, 199289, 199313, 199321, 199337, 199343, 199357, 199373, 199379, 199399, 199403, 199411, 199417, 199429, 199447, 199453, 199457, 199483, 199487, 199489, 199499, 199501, 199523, 199559, 199567, 199583, 199601, 199603, 199621, 199637, 199657, 199669, 199673, 199679, 199687, 199697, 199721, 199729, 199739, 199741, 199751, 199753, 199777, 199783, 199799, 199807, 199811, 199813, 199819, 199831, 199853, 199873, 199877, 199889, 199909, 199921, 199931, 199933, 199961, 199967, 199999};
		for(int i = 0,len=a.length;i<len;i++){
			prime.add(a[i]);
			primeMap.put(a[i], true);
		}
	}
	
	private static void init100000(){
		int[] a = new int[]{100003, 100019, 100043, 100049, 100057, 100069, 100103, 100109, 100129, 100151, 100153, 100169, 100183, 100189, 100193, 100207, 100213, 100237, 100267, 100271, 100279, 100291, 100297, 100313, 100333, 100343, 100357, 100361, 100363, 100379, 100391, 100393, 100403, 100411, 100417, 100447, 100459, 100469, 100483, 100493, 100501, 100511, 100517, 100519, 100523, 100537, 100547, 100549, 100559, 100591, 100609, 100613, 100621, 100649, 100669, 100673, 100693, 100699, 100703, 100733, 100741, 100747, 100769, 100787, 100799, 100801, 100811, 100823, 100829, 100847, 100853, 100907, 100913, 100927, 100931, 100937, 100943, 100957, 100981, 100987, 100999, 101009, 101021, 101027, 101051, 101063, 101081, 101089, 101107, 101111, 101113, 101117, 101119, 101141, 101149, 101159, 101161, 101173, 101183, 101197, 101203, 101207, 101209, 101221, 101267, 101273, 101279, 101281, 101287, 101293, 101323, 101333, 101341, 101347, 101359, 101363, 101377, 101383, 101399, 101411, 101419, 101429, 101449, 101467, 101477, 101483, 101489, 101501, 101503, 101513, 101527, 101531, 101533, 101537, 101561, 101573, 101581, 101599, 101603, 101611, 101627, 101641, 101653, 101663, 101681, 101693, 101701, 101719, 101723, 101737, 101741, 101747, 101749, 101771, 101789, 101797, 101807, 101833, 101837, 101839, 101863, 101869, 101873, 101879, 101891, 101917, 101921, 101929, 101939, 101957, 101963, 101977, 101987, 101999, 102001, 102013, 102019, 102023, 102031, 102043, 102059, 102061, 102071, 102077, 102079, 102101, 102103, 102107, 102121, 102139, 102149, 102161, 102181, 102191, 102197, 102199, 102203, 102217, 102229, 102233, 102241, 102251, 102253, 102259, 102293, 102299, 102301, 102317, 102329, 102337, 102359, 102367, 102397, 102407, 102409, 102433, 102437, 102451, 102461, 102481, 102497, 102499, 102503, 102523, 102533, 102539, 102547, 102551, 102559, 102563, 102587, 102593, 102607, 102611, 102643, 102647, 102653, 102667, 102673, 102677, 102679, 102701, 102761, 102763, 102769, 102793, 102797, 102811, 102829, 102841, 102859, 102871, 102877, 102881, 102911, 102913, 102929, 102931, 102953, 102967, 102983, 103001, 103007, 103043, 103049, 103067, 103069, 103079, 103087, 103091, 103093, 103099, 103123, 103141, 103171, 103177, 103183, 103217, 103231, 103237, 103289, 103291, 103307, 103319, 103333, 103349, 103357, 103387, 103391, 103393, 103399, 103409, 103421, 103423, 103451, 103457, 103471, 103483, 103511, 103529, 103549, 103553, 103561, 103567, 103573, 103577, 103583, 103591, 103613, 103619, 103643, 103651, 103657, 103669, 103681, 103687, 103699, 103703, 103723, 103769, 103787, 103801, 103811, 103813, 103837, 103841, 103843, 103867, 103889, 103903, 103913, 103919, 103951, 103963, 103967, 103969, 103979, 103981, 103991, 103993, 103997, 104003, 104009, 104021, 104033, 104047, 104053, 104059, 104087, 104089, 104107, 104113, 104119, 104123, 104147, 104149, 104161, 104173, 104179, 104183, 104207, 104231, 104233, 104239, 104243, 104281, 104287, 104297, 104309, 104311, 104323, 104327, 104347, 104369, 104381, 104383, 104393, 104399, 104417, 104459, 104471, 104473, 104479, 104491, 104513, 104527, 104537, 104543, 104549, 104551, 104561, 104579, 104593, 104597, 104623, 104639, 104651, 104659, 104677, 104681, 104683, 104693, 104701, 104707, 104711, 104717, 104723, 104729, 104743, 104759, 104761, 104773, 104779, 104789, 104801, 104803, 104827, 104831, 104849, 104851, 104869, 104879, 104891, 104911, 104917, 104933, 104947, 104953, 104959, 104971, 104987, 104999};
		for(int i = 0,len=a.length;i<len;i++){
			prime.add(a[i]);
			primeMap.put(a[i], true);
		}
	}
	private static void init99999(){
		for(int i=2;i<100000;i++){
			if( isPrime(i)){
				prime.add(i);
				primeMap.put(i, true);
			}
		}
	}
	
	private static boolean isPrime(int n) {
		int t = (int)Math.sqrt(n);
		for(int i=2;i<=t;i++) {
			if( n% i == 0) {
				return false;
			}
		}
		return true;
	}

	private static void init() {
//		long t1 = System.currentTimeMillis();
		primeMap.put(1, true);
		init99999();
		init100000();
		init100500();
		init200000();
		init300000();
		init400000();
		init500000();
		init600000();
		init700000();
		init800000();
		init900000();
//		System.out.println(System.currentTimeMillis()-t1);
	}
}