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.math.BigInteger;
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);
		}

		BigInteger t = BigInteger.ONE;
		for(Integer p:maxMap.keySet()) {
			int count = maxMap.get(p);
			
			t = t .multiply(BigInteger.valueOf(pow(p,count)));
		}
		
		long sum = 0;
		for(int i=0;i<N;i++) {
			
//			BigInteger s  = t.divide(BigInteger.valueOf(arr[i]/commonGcd)).mod(BigInteger.valueOf(1000000007));
//			sum = (sum + s.longValue()) %1000000007;
		}
		System.out.println(sum);
	}

	private static long pow(int a, int p) {
		if (p == 1) {
			return a;
		}
		if (p == 0) {
			return 1;
		}
		if( p == 2){
			return a*a;
		}
		int res = 1;
		int p2 = a * a;
		int p3 = p2 *a ;
		for (int t = 3; t <= p; t += 3) {
			res = res * p3;
		}
		res = res * (p % 3 == 1 ? a : p%3==2?p2:1);
		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, 911593, 911597, 911621, 911633, 911657, 911663, 911671, 911681, 911683, 911689, 911707, 911719, 911723, 911737, 911749, 911773, 911777, 911783, 911819, 911831, 911837, 911839, 911851, 911861, 911873, 911879, 911893, 911899, 911903, 911917, 911947, 911951, 911957, 911959, 911969, 912007, 912031, 912047, 912049, 912053, 912061, 912083, 912089, 912103, 912167, 912173, 912187, 912193, 912211, 912217, 912227, 912239, 912251, 912269, 912287, 912337, 912343, 912349, 912367, 912391, 912397, 912403, 912409, 912413, 912449, 912451, 912463, 912467, 912469, 912481, 912487, 912491, 912497, 912511, 912521, 912523, 912533, 912539, 912559, 912581, 912631, 912647, 912649, 912727, 912763, 912773, 912797, 912799, 912809, 912823, 912829, 912839, 912851, 912853, 912859, 912869, 912871, 912911, 912929, 912941, 912953, 912959, 912971, 912973, 912979, 912991, 913013, 913027, 913037, 913039, 913063, 913067, 913103, 913139, 913151, 913177, 913183, 913217, 913247, 913259, 913279, 913309, 913321, 913327, 913331, 913337, 913373, 913397, 913417, 913421, 913433, 913441, 913447, 913457, 913483, 913487, 913513, 913571, 913573, 913579, 913589, 913637, 913639, 913687, 913709, 913723, 913739, 913753, 913771, 913799, 913811, 913853, 913873, 913889, 913907, 913921, 913933, 913943, 913981, 913999, 914021, 914027, 914041, 914047, 914117, 914131, 914161, 914189, 914191, 914213, 914219, 914237, 914239, 914257, 914269, 914279, 914293, 914321, 914327, 914339, 914351, 914357, 914359, 914363, 914369, 914371, 914429, 914443, 914449, 914461, 914467, 914477, 914491, 914513, 914519, 914521, 914533, 914561, 914569, 914579, 914581, 914591, 914597, 914609, 914611, 914629, 914647, 914657, 914701, 914713, 914723, 914731, 914737, 914777, 914783, 914789, 914791, 914801, 914813, 914819, 914827, 914843, 914857, 914861, 914867, 914873, 914887, 914891, 914897, 914941, 914951, 914971, 914981, 915007, 915017, 915029, 915041, 915049, 915053, 915067, 915071, 915113, 915139, 915143, 915157, 915181, 915191, 915197, 915199, 915203, 915221, 915223, 915247, 915251, 915253, 915259, 915283, 915301, 915311, 915353, 915367, 915379, 915391, 915437, 915451, 915479, 915487, 915527, 915533, 915539, 915547, 915557, 915587, 915589, 915601, 915611, 915613, 915623, 915631, 915641, 915659, 915683, 915697, 915703, 915727, 915731, 915737, 915757, 915763, 915769, 915799, 915839, 915851, 915869, 915881, 915911, 915917, 915919, 915947, 915949, 915961, 915973, 915991, 916031, 916033, 916049, 916057, 916061, 916073, 916099, 916103, 916109, 916121, 916127, 916129, 916141, 916169, 916177, 916183, 916187, 916189, 916213, 916217, 916219, 916259, 916261, 916273, 916291, 916319, 916337, 916339, 916361, 916367, 916387, 916411, 916417, 916441, 916451, 916457, 916463, 916469, 916471, 916477, 916501, 916507, 916511, 916537, 916561, 916571, 916583, 916613, 916621, 916633, 916649, 916651, 916679, 916703, 916733, 916771, 916781, 916787, 916831, 916837, 916841, 916859, 916871, 916879, 916907, 916913, 916931, 916933, 916939, 916961, 916973, 916999, 917003, 917039, 917041, 917051, 917053, 917083, 917089, 917093, 917101, 917113, 917117, 917123, 917141, 917153, 917159, 917173, 917179, 917209, 917219, 917227, 917237, 917239, 917243, 917251, 917281, 917291, 917317, 917327, 917333, 917353, 917363, 917381, 917407, 917443, 917459, 917461, 917471, 917503, 917513, 917519, 917549, 917557, 917573, 917591, 917593, 917611, 917617, 917629, 917633, 917641, 917659, 917669, 917687, 917689, 917713, 917729, 917737, 917753, 917759, 917767, 917771, 917773, 917783, 917789, 917803, 917809, 917827, 917831, 917837, 917843, 917849, 917869, 917887, 917893, 917923, 917927, 917951, 917971, 917993, 918011, 918019, 918041, 918067, 918079, 918089, 918103, 918109, 918131, 918139, 918143, 918149, 918157, 918161, 918173, 918193, 918199, 918209, 918223, 918257, 918259, 918263, 918283, 918301, 918319, 918329, 918341, 918347, 918353, 918361, 918371, 918389, 918397, 918431, 918433, 918439, 918443, 918469, 918481, 918497, 918529, 918539, 918563, 918581, 918583, 918587, 918613, 918641, 918647, 918653, 918677, 918679, 918683, 918733, 918737, 918751, 918763, 918767, 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995167, 995173, 995219, 995227, 995237, 995243, 995273, 995303, 995327, 995329, 995339, 995341, 995347, 995363, 995369, 995377, 995381, 995387, 995399, 995431, 995443, 995447, 995461, 995471, 995513, 995531, 995539, 995549, 995551, 995567, 995573, 995587, 995591, 995593, 995611, 995623, 995641, 995651, 995663, 995669, 995677, 995699, 995713, 995719, 995737, 995747, 995783, 995791, 995801, 995833, 995881, 995887, 995903, 995909, 995927, 995941, 995957, 995959, 995983, 995987, 995989, 996001, 996011, 996019, 996049, 996067, 996103, 996109, 996119, 996143, 996157, 996161, 996167, 996169, 996173, 996187, 996197, 996209, 996211, 996253, 996257, 996263, 996271, 996293, 996301, 996311, 996323, 996329, 996361, 996367, 996403, 996407, 996409, 996431, 996461, 996487, 996511, 996529, 996539, 996551, 996563, 996571, 996599, 996601, 996617, 996629, 996631, 996637, 996647, 996649, 996689, 996703, 996739, 996763, 996781, 996803, 996811, 996841, 996847, 996857, 996859, 996871, 996881, 996883, 996887, 996899, 996953, 996967, 996973, 996979, 997001, 997013, 997019, 997021, 997037, 997043, 997057, 997069, 997081, 997091, 997097, 997099, 997103, 997109, 997111, 997121, 997123, 997141, 997147, 997151, 997153, 997163, 997201, 997207, 997219, 997247, 997259, 997267, 997273, 997279, 997307, 997309, 997319, 997327, 997333, 997343, 997357, 997369, 997379, 997391, 997427, 997433, 997439, 997453, 997463, 997511, 997541, 997547, 997553, 997573, 997583, 997589, 997597, 997609, 997627, 997637, 997649, 997651, 997663, 997681, 997693, 997699, 997727, 997739, 997741, 997751, 997769, 997783, 997793, 997807, 997811, 997813, 997877, 997879, 997889, 997891, 997897, 997933, 997949, 997961, 997963, 997973, 997991, 998009, 998017, 998027, 998029, 998069, 998071, 998077, 998083, 998111, 998117, 998147, 998161, 998167, 998197, 998201, 998213, 998219, 998237, 998243, 998273, 998281, 998287, 998311, 998329, 998353, 998377, 998381, 998399, 998411, 998419, 998423, 998429, 998443, 998471, 998497, 998513, 998527, 998537, 998539, 998551, 998561, 998617, 998623, 998629, 998633, 998651, 998653, 998681, 998687, 998689, 998717, 998737, 998743, 998749, 998759, 998779, 998813, 998819, 998831, 998839, 998843, 998857, 998861, 998897, 998909, 998917, 998927, 998941, 998947, 998951, 998957, 998969, 998983, 998989, 999007, 999023, 999029, 999043, 999049, 999067, 999083, 999091, 999101, 999133, 999149, 999169, 999181, 999199, 999217, 999221, 999233, 999239, 999269, 999287, 999307, 999329, 999331, 999359, 999371, 999377, 999389, 999431, 999433, 999437, 999451, 999491, 999499, 999521, 999529, 999541, 999553, 999563, 999599, 999611, 999613, 999623, 999631, 999653, 999667, 999671, 999683, 999721, 999727, 999749, 999763, 999769, 999773, 999809, 999853, 999863, 999883, 999907, 999917, 999931, 999953, 999959, 999961, 999979, 999983};
		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, 810223, 810239, 810253, 810259, 810269, 810281, 810307, 810319, 810343, 810349, 810353, 810361, 810367, 810377, 810379, 810389, 810391, 810401, 810409, 810419, 810427, 810437, 810443, 810457, 810473, 810487, 810493, 810503, 810517, 810533, 810539, 810541, 810547, 810553, 810571, 810581, 810583, 810587, 810643, 810653, 810659, 810671, 810697, 810737, 810757, 810763, 810769, 810791, 810809, 810839, 810853, 810871, 810881, 810893, 810907, 810913, 810923, 810941, 810949, 810961, 810967, 810973, 810989, 811037, 811039, 811067, 811081, 811099, 811123, 811127, 811147, 811157, 811163, 811171, 811183, 811193, 811199, 811207, 811231, 811241, 811253, 811259, 811273, 811277, 811289, 811297, 811337, 811351, 811379, 811387, 811411, 811429, 811441, 811457, 811469, 811493, 811501, 811511, 811519, 811523, 811553, 811561, 811583, 811607, 811619, 811627, 811637, 811649, 811651, 811667, 811691, 811697, 811703, 811709, 811729, 811747, 811753, 811757, 811763, 811771, 811777, 811799, 811819, 811861, 811871, 811879, 811897, 811919, 811931, 811933, 811957, 811961, 811981, 811991, 811997, 812011, 812033, 812047, 812051, 812057, 812081, 812101, 812129, 812137, 812167, 812173, 812179, 812183, 812191, 812213, 812221, 812233, 812249, 812257, 812267, 812281, 812297, 812299, 812309, 812341, 812347, 812351, 812353, 812359, 812363, 812381, 812387, 812393, 812401, 812431, 812443, 812467, 812473, 812477, 812491, 812501, 812503, 812519, 812527, 812587, 812597, 812599, 812627, 812633, 812639, 812641, 812671, 812681, 812689, 812699, 812701, 812711, 812717, 812731, 812759, 812761, 812807, 812849, 812857, 812869, 812921, 812939, 812963, 812969, 813013, 813017, 813023, 813041, 813049, 813061, 813083, 813089, 813091, 813097, 813107, 813121, 813133, 813157, 813167, 813199, 813203, 813209, 813217, 813221, 813227, 813251, 813269, 813277, 813283, 813287, 813299, 813301, 813311, 813343, 813361, 813367, 813377, 813383, 813401, 813419, 813427, 813443, 813493, 813499, 813503, 813511, 813529, 813541, 813559, 813577, 813583, 813601, 813613, 813623, 813647, 813677, 813697, 813707, 813721, 813749, 813767, 813797, 813811, 813817, 813829, 813833, 813847, 813863, 813871, 813893, 813907, 813931, 813961, 813971, 813991, 813997, 814003, 814007, 814013, 814019, 814031, 814043, 814049, 814061, 814063, 814067, 814069, 814081, 814097, 814127, 814129, 814139, 814171, 814183, 814193, 814199, 814211, 814213, 814237, 814241, 814243, 814279, 814309, 814327, 814337, 814367, 814379, 814381, 814393, 814399, 814403, 814423, 814447, 814469, 814477, 814493, 814501, 814531, 814537, 814543, 814559, 814577, 814579, 814601, 814603, 814609, 814631, 814633, 814643, 814687, 814699, 814717, 814741, 814747, 814763, 814771, 814783, 814789, 814799, 814823, 814829, 814841, 814859, 814873, 814883, 814889, 814901, 814903, 814927, 814937, 814939, 814943, 814949, 814991, 815029, 815033, 815047, 815053, 815063, 815123, 815141, 815149, 815159, 815173, 815197, 815209, 815231, 815251, 815257, 815261, 815273, 815279, 815291, 815317, 815333, 815341, 815351, 815389, 815401, 815411, 815413, 815417, 815431, 815453, 815459, 815471, 815491, 815501, 815519, 815527, 815533, 815539, 815543, 815569, 815587, 815599, 815621, 815623, 815627, 815653, 815663, 815669, 815671, 815681, 815687, 815693, 815713, 815729, 815809, 815819, 815821, 815831, 815851, 815869, 815891, 815897, 815923, 815933, 815939, 815953, 815963, 815977, 815989, 816019, 816037, 816043, 816047, 816077, 816091, 816103, 816113, 816121, 816131, 816133, 816157, 816161, 816163, 816169, 816191, 816203, 816209, 816217, 816223, 816227, 816239, 816251, 816271, 816317, 816329, 816341, 816353, 816367, 816377, 816401, 816427, 816443, 816451, 816469, 816499, 816521, 816539, 816547, 816559, 816581, 816587, 816589, 816593, 816649, 816653, 816667, 816689, 816691, 816703, 816709, 816743, 816763, 816769, 816779, 816811, 816817, 816821, 816839, 816841, 816847, 816857, 816859, 816869, 816883, 816887, 816899, 816911, 816917, 816919, 816929, 816941, 816947, 816961, 816971, 817013, 817027, 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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, 706547, 706561, 706597, 706603, 706613, 706621, 706631, 706633, 706661, 706669, 706679, 706703, 706709, 706729, 706733, 706747, 706751, 706753, 706757, 706763, 706787, 706793, 706801, 706829, 706837, 706841, 706847, 706883, 706897, 706907, 706913, 706919, 706921, 706943, 706961, 706973, 706987, 706999, 707011, 707027, 707029, 707053, 707071, 707099, 707111, 707117, 707131, 707143, 707153, 707159, 707177, 707191, 707197, 707219, 707249, 707261, 707279, 707293, 707299, 707321, 707341, 707359, 707383, 707407, 707429, 707431, 707437, 707459, 707467, 707501, 707527, 707543, 707561, 707563, 707573, 707627, 707633, 707647, 707653, 707669, 707671, 707677, 707683, 707689, 707711, 707717, 707723, 707747, 707753, 707767, 707789, 707797, 707801, 707813, 707827, 707831, 707849, 707857, 707869, 707873, 707887, 707911, 707923, 707929, 707933, 707939, 707951, 707953, 707957, 707969, 707981, 707983, 708007, 708011, 708017, 708023, 708031, 708041, 708047, 708049, 708053, 708061, 708091, 708109, 708119, 708131, 708137, 708139, 708161, 708163, 708179, 708199, 708221, 708223, 708229, 708251, 708269, 708283, 708287, 708293, 708311, 708329, 708343, 708347, 708353, 708359, 708361, 708371, 708403, 708437, 708457, 708473, 708479, 708481, 708493, 708497, 708517, 708527, 708559, 708563, 708569, 708583, 708593, 708599, 708601, 708641, 708647, 708667, 708689, 708703, 708733, 708751, 708803, 708823, 708839, 708857, 708859, 708893, 708899, 708907, 708913, 708923, 708937, 708943, 708959, 708979, 708989, 708991, 708997, 709043, 709057, 709097, 709117, 709123, 709139, 709141, 709151, 709153, 709157, 709201, 709211, 709217, 709231, 709237, 709271, 709273, 709279, 709283, 709307, 709321, 709337, 709349, 709351, 709381, 709409, 709417, 709421, 709433, 709447, 709451, 709453, 709469, 709507, 709519, 709531, 709537, 709547, 709561, 709589, 709603, 709607, 709609, 709649, 709651, 709663, 709673, 709679, 709691, 709693, 709703, 709729, 709739, 709741, 709769, 709777, 709789, 709799, 709817, 709823, 709831, 709843, 709847, 709853, 709861, 709871, 709879, 709901, 709909, 709913, 709921, 709927, 709957, 709963, 709967, 709981, 709991, 710009, 710023, 710027, 710051, 710053, 710081, 710089, 710119, 710189, 710207, 710219, 710221, 710257, 710261, 710273, 710293, 710299, 710321, 710323, 710327, 710341, 710351, 710371, 710377, 710383, 710389, 710399, 710441, 710443, 710449, 710459, 710473, 710483, 710491, 710503, 710513, 710519, 710527, 710531, 710557, 710561, 710569, 710573, 710599, 710603, 710609, 710621, 710623, 710627, 710641, 710663, 710683, 710693, 710713, 710777, 710779, 710791, 710813, 710837, 710839, 710849, 710851, 710863, 710867, 710873, 710887, 710903, 710909, 710911, 710917, 710929, 710933, 710951, 710959, 710971, 710977, 710987, 710989, 711001, 711017, 711019, 711023, 711041, 711049, 711089, 711097, 711121, 711131, 711133, 711143, 711163, 711173, 711181, 711187, 711209, 711223, 711259, 711287, 711299, 711307, 711317, 711329, 711353, 711371, 711397, 711409, 711427, 711437, 711463, 711479, 711497, 711499, 711509, 711517, 711523, 711539, 711563, 711577, 711583, 711589, 711617, 711629, 711649, 711653, 711679, 711691, 711701, 711707, 711709, 711713, 711727, 711731, 711749, 711751, 711757, 711793, 711811, 711817, 711829, 711839, 711847, 711859, 711877, 711889, 711899, 711913, 711923, 711929, 711937, 711947, 711959, 711967, 711973, 711983, 712007, 712021, 712051, 712067, 712093, 712109, 712121, 712133, 712157, 712169, 712171, 712183, 712199, 712219, 712237, 712279, 712289, 712301, 712303, 712319, 712321, 712331, 712339, 712357, 712409, 712417, 712427, 712429, 712433, 712447, 712477, 712483, 712489, 712493, 712499, 712507, 712511, 712531, 712561, 712571, 712573, 712601, 712603, 712631, 712651, 712669, 712681, 712687, 712693, 712697, 712711, 712717, 712739, 712781, 712807, 712819, 712837, 712841, 712843, 712847, 712883, 712889, 712891, 712909, 712913, 712927, 712939, 712951, 712961, 712967, 712973, 712981, 713021, 713039, 713059, 713077, 713107, 713117, 713129, 713147, 713149, 713159, 713171, 713177, 713183, 713189, 713191, 713227, 713233, 713239, 713243, 713261, 713267, 713281, 713287, 713309, 713311, 713329, 713347, 713351, 713353, 713357, 713381, 713389, 713399, 713407, 713411, 713417, 713467, 713477, 713491, 713497, 713501, 713509, 713533, 713563, 713569, 713597, 713599, 713611, 713627, 713653, 713663, 713681, 713737, 713743, 713747, 713753, 713771, 713807, 713827, 713831, 713833, 713861, 713863, 713873, 713891, 713903, 713917, 713927, 713939, 713941, 713957, 713981, 713987, 714029, 714037, 714061, 714073, 714107, 714113, 714139, 714143, 714151, 714163, 714169, 714199, 714223, 714227, 714247, 714257, 714283, 714341, 714349, 714361, 714377, 714443, 714463, 714479, 714481, 714487, 714503, 714509, 714517, 714521, 714529, 714551, 714557, 714563, 714569, 714577, 714601, 714619, 714673, 714677, 714691, 714719, 714739, 714751, 714773, 714781, 714787, 714797, 714809, 714827, 714839, 714841, 714851, 714853, 714869, 714881, 714887, 714893, 714907, 714911, 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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, 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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, 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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, 405143, 405157, 405179, 405199, 405211, 405221, 405227, 405239, 405241, 405247, 405253, 405269, 405277, 405287, 405299, 405323, 405341, 405343, 405347, 405373, 405401, 405407, 405413, 405437, 405439, 405473, 405487, 405491, 405497, 405499, 405521, 405527, 405529, 405541, 405553, 405577, 405599, 405607, 405611, 405641, 405659, 405667, 405677, 405679, 405683, 405689, 405701, 405703, 405709, 405719, 405731, 405749, 405763, 405767, 405781, 405799, 405817, 405827, 405829, 405857, 405863, 405869, 405871, 405893, 405901, 405917, 405947, 405949, 405959, 405967, 405989, 405991, 405997, 406013, 406027, 406037, 406067, 406073, 406093, 406117, 406123, 406169, 406171, 406177, 406183, 406207, 406247, 406253, 406267, 406271, 406309, 406313, 406327, 406331, 406339, 406349, 406361, 406381, 406397, 406403, 406423, 406447, 406481, 406499, 406501, 406507, 406513, 406517, 406531, 406547, 406559, 406561, 406573, 406577, 406579, 406583, 406591, 406631, 406633, 406649, 406661, 406673, 406697, 406699, 406717, 406729, 406739, 406789, 406807, 406811, 406817, 406837, 406859, 406873, 406883, 406907, 406951, 406969, 406981, 406993, 407023, 407047, 407059, 407083, 407119, 407137, 407149, 407153, 407177, 407179, 407191, 407203, 407207, 407219, 407221, 407233, 407249, 407257, 407263, 407273, 407287, 407291, 407299, 407311, 407317, 407321, 407347, 407357, 407359, 407369, 407377, 407383, 407401, 407437, 407471, 407483, 407489, 407501, 407503, 407509, 407521, 407527, 407567, 407573, 407579, 407587, 407599, 407621, 407633, 407639, 407651, 407657, 407669, 407699, 407707, 407713, 407717, 407723, 407741, 407747, 407783, 407789, 407791, 407801, 407807, 407821, 407833, 407843, 407857, 407861, 407879, 407893, 407899, 407917, 407923, 407947, 407959, 407969, 407971, 407977, 407993, 408011, 408019, 408041, 408049, 408071, 408077, 408091, 408127, 408131, 408137, 408169, 408173, 408197, 408203, 408209, 408211, 408217, 408223, 408229, 408241, 408251, 408263, 408271, 408283, 408311, 408337, 408341, 408347, 408361, 408379, 408389, 408403, 408413, 408427, 408431, 408433, 408437, 408461, 408469, 408479, 408491, 408497, 408533, 408539, 408553, 408563, 408607, 408623, 408631, 408637, 408643, 408659, 408677, 408689, 408691, 408701, 408703, 408713, 408719, 408743, 408763, 408769, 408773, 408787, 408803, 408809, 408817, 408841, 408857, 408869, 408911, 408913, 408923, 408943, 408953, 408959, 408971, 408979, 408997, 409007, 409021, 409027, 409033, 409043, 409063, 409069, 409081, 409099, 409121, 409153, 409163, 409177, 409187, 409217, 409237, 409259, 409261, 409267, 409271, 409289, 409291, 409327, 409333, 409337, 409349, 409351, 409369, 409379, 409391, 409397, 409429, 409433, 409441, 409463, 409471, 409477, 409483, 409499, 409517, 409523, 409529, 409543, 409573, 409579, 409589, 409597, 409609, 409639, 409657, 409691, 409693, 409709, 409711, 409723, 409729, 409733, 409753, 409769, 409777, 409781, 409813, 409817, 409823, 409831, 409841, 409861, 409867, 409879, 409889, 409891, 409897, 409901, 409909, 409933, 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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, 307609, 307627, 307631, 307633, 307639, 307651, 307669, 307687, 307691, 307693, 307711, 307733, 307759, 307817, 307823, 307831, 307843, 307859, 307871, 307873, 307891, 307903, 307919, 307939, 307969, 308003, 308017, 308027, 308041, 308051, 308081, 308093, 308101, 308107, 308117, 308129, 308137, 308141, 308149, 308153, 308213, 308219, 308249, 308263, 308291, 308293, 308303, 308309, 308311, 308317, 308323, 308327, 308333, 308359, 308383, 308411, 308423, 308437, 308447, 308467, 308489, 308491, 308501, 308507, 308509, 308519, 308521, 308527, 308537, 308551, 308569, 308573, 308587, 308597, 308621, 308639, 308641, 308663, 308681, 308701, 308713, 308723, 308761, 308773, 308801, 308809, 308813, 308827, 308849, 308851, 308857, 308887, 308899, 308923, 308927, 308929, 308933, 308939, 308951, 308989, 308999, 309007, 309011, 309013, 309019, 309031, 309037, 309059, 309079, 309083, 309091, 309107, 309109, 309121, 309131, 309137, 309157, 309167, 309173, 309193, 309223, 309241, 309251, 309259, 309269, 309271, 309277, 309289, 309293, 309311, 309313, 309317, 309359, 309367, 309371, 309391, 309403, 309433, 309437, 309457, 309461, 309469, 309479, 309481, 309493, 309503, 309521, 309523, 309539, 309541, 309559, 309571, 309577, 309583, 309599, 309623, 309629, 309637, 309667, 309671, 309677, 309707, 309713, 309731, 309737, 309769, 309779, 309781, 309797, 309811, 309823, 309851, 309853, 309857, 309877, 309899, 309929, 309931, 309937, 309977, 309989, 310019, 310021, 310027, 310043, 310049, 310081, 310087, 310091, 310111, 310117, 310127, 310129, 310169, 310181, 310187, 310223, 310229, 310231, 310237, 310243, 310273, 310283, 310291, 310313, 310333, 310357, 310361, 310363, 310379, 310397, 310423, 310433, 310439, 310447, 310459, 310463, 310481, 310489, 310501, 310507, 310511, 310547, 310553, 310559, 310567, 310571, 310577, 310591, 310627, 310643, 310663, 310693, 310697, 310711, 310721, 310727, 310729, 310733, 310741, 310747, 310771, 310781, 310789, 310801, 310819, 310823, 310829, 310831, 310861, 310867, 310883, 310889, 310901, 310927, 310931, 310949, 310969, 310987, 310997, 311009, 311021, 311027, 311033, 311041, 311099, 311111, 311123, 311137, 311153, 311173, 311177, 311183, 311189, 311197, 311203, 311237, 311279, 311291, 311293, 311299, 311303, 311323, 311329, 311341, 311347, 311359, 311371, 311393, 311407, 311419, 311447, 311453, 311473, 311533, 311537, 311539, 311551, 311557, 311561, 311567, 311569, 311603, 311609, 311653, 311659, 311677, 311681, 311683, 311687, 311711, 311713, 311737, 311743, 311747, 311749, 311791, 311803, 311807, 311821, 311827, 311867, 311869, 311881, 311897, 311951, 311957, 311963, 311981, 312007, 312023, 312029, 312031, 312043, 312047, 312071, 312073, 312083, 312089, 312101, 312107, 312121, 312161, 312197, 312199, 312203, 312209, 312211, 312217, 312229, 312233, 312241, 312251, 312253, 312269, 312281, 312283, 312289, 312311, 312313, 312331, 312343, 312349, 312353, 312371, 312383, 312397, 312401, 312407, 312413, 312427, 312451, 312469, 312509, 312517, 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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, 209201, 209203, 209213, 209221, 209227, 209233, 209249, 209257, 209263, 209267, 209269, 209299, 209311, 209317, 209327, 209333, 209347, 209353, 209357, 209359, 209371, 209381, 209393, 209401, 209431, 209441, 209449, 209459, 209471, 209477, 209497, 209519, 209533, 209543, 209549, 209563, 209567, 209569, 209579, 209581, 209597, 209621, 209623, 209639, 209647, 209659, 209669, 209687, 209701, 209707, 209717, 209719, 209743, 209767, 209771, 209789, 209801, 209809, 209813, 209819, 209821, 209837, 209851, 209857, 209861, 209887, 209917, 209927, 209929, 209939, 209953, 209959, 209971, 209977, 209983, 209987, 210011, 210019, 210031, 210037, 210053, 210071, 210097, 210101, 210109, 210113, 210127, 210131, 210139, 210143, 210157, 210169, 210173, 210187, 210191, 210193, 210209, 210229, 210233, 210241, 210247, 210257, 210263, 210277, 210283, 210299, 210317, 210319, 210323, 210347, 210359, 210361, 210391, 210401, 210403, 210407, 210421, 210437, 210461, 210467, 210481, 210487, 210491, 210499, 210523, 210527, 210533, 210557, 210599, 210601, 210619, 210631, 210643, 210659, 210671, 210709, 210713, 210719, 210731, 210739, 210761, 210773, 210803, 210809, 210811, 210823, 210827, 210839, 210853, 210857, 210869, 210901, 210907, 210911, 210913, 210923, 210929, 210943, 210961, 210967, 211007, 211039, 211049, 211051, 211061, 211063, 211067, 211073, 211093, 211097, 211129, 211151, 211153, 211177, 211187, 211193, 211199, 211213, 211217, 211219, 211229, 211231, 211241, 211247, 211271, 211283, 211291, 211297, 211313, 211319, 211333, 211339, 211349, 211369, 211373, 211403, 211427, 211433, 211441, 211457, 211469, 211493, 211499, 211501, 211507, 211543, 211559, 211571, 211573, 211583, 211597, 211619, 211639, 211643, 211657, 211661, 211663, 211681, 211691, 211693, 211711, 211723, 211727, 211741, 211747, 211777, 211781, 211789, 211801, 211811, 211817, 211859, 211867, 211873, 211877, 211879, 211889, 211891, 211927, 211931, 211933, 211943, 211949, 211969, 211979, 211997, 212029, 212039, 212057, 212081, 212099, 212117, 212123, 212131, 212141, 212161, 212167, 212183, 212203, 212207, 212209, 212227, 212239, 212243, 212281, 212293, 212297, 212353, 212369, 212383, 212411, 212419, 212423, 212437, 212447, 212453, 212461, 212467, 212479, 212501, 212507, 212557, 212561, 212573, 212579, 212587, 212593, 212627, 212633, 212651, 212669, 212671, 212677, 212683, 212701, 212777, 212791, 212801, 212827, 212837, 212843, 212851, 212867, 212869, 212873, 212881, 212897, 212903, 212909, 212917, 212923, 212969, 212981, 212987, 212999, 213019, 213023, 213029, 213043, 213067, 213079, 213091, 213097, 213119, 213131, 213133, 213139, 213149, 213173, 213181, 213193, 213203, 213209, 213217, 213223, 213229, 213247, 213253, 213263, 213281, 213287, 213289, 213307, 213319, 213329, 213337, 213349, 213359, 213361, 213383, 213391, 213397, 213407, 213449, 213461, 213467, 213481, 213491, 213523, 213533, 213539, 213553, 213557, 213589, 213599, 213611, 213613, 213623, 213637, 213641, 213649, 213659, 213713, 213721, 213727, 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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 init99999(){
		for(int i=2;i<200000;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 t = System.currentTimeMillis();
		primeMap.put(1, true);
		init99999();
		init200000();
		init300000();
		init400000();
		init500000();
		init600000();
		init700000();
		init800000();
		init900000();
//		System.out.println(System.currentTimeMillis() -t);
	}
}