Problem: You are given two positive integers a and b. There are two possible operations: 

  1. multiply one of the numbers by some prime p; 
  2. divide one of the numbers on its prime factor p. 



What is the minimum number of operations required to obtain two integers having the same number of divisors? You are given several such pairs, you need to find the answer for each of them.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of pairs of integers for which you are to find the answer.

Each of the next t lines contain two integers a_i and b_i (1 ≤ a_i, b_i ≤ 10^6).

Output

Output t lines — the i-th of them should contain the answer for the pair a_i, b_i.

Example

Input

8
9 10
100 17
220 70
17 19
4 18
32 20
100 32
224 385


Output

1
3
1
0
1
0
1
1

Note

These are the numbers with equal number of divisors, which are optimal to obtain in the sample test case: 

  * (27, 10), 4 divisors 
  * (100, 1156), 9 divisors 
  * (220, 140), 12 divisors 
  * (17, 19), 2 divisors 
  * (12, 18), 6 divisors 
  * (50, 32), 6 divisors 
  * (224, 1925), 12 divisors 



Note that there can be several optimal pairs of numbers.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.Map.Entry;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class Techno19_2F {

	static int MODE = -1;

	static final Comparator<int[]> COMP_ARR = new Comparator<int[]>() {
		public int compare(int[] a1, int[] a2) {
			if (MODE != -1 && (a1.length == 32 || a2.length == 32)) {
				if (a1.length == 32) {
					if (MODE < a2.length) {
						return -1;
					}
					if (MODE > a2.length) {
						return 1;
					}
				} else {
					if (a1.length < MODE) {
						return -1;
					}
					if (a1.length > MODE) {
						return 1;
					}
				}

				for (int i = 0; i < MODE; i++) {
					if (a1[i] < a2[i]) {
						return -1;
					}
					if (a1[i] > a2[i]) {
						return 1;
					}
				}
				return 0;
			} else {
				if (a1.length < a2.length) {
					return -1;
				}
				if (a1.length > a2.length) {
					return 1;
				}

				for (int i = 0; i < a2.length; i++) {
					if (a1[i] < a2[i]) {
						return -1;
					}
					if (a1[i] > a2[i]) {
						return 1;
					}
				}
				return 0;
			}
		}
	};

	static TreeMap<int[], Integer> index = new TreeMap<>(COMP_ARR);
	static int[][] states;

	static ArrayList<int[]> start = new ArrayList<>();

	static int[] numD;

	static int[] pFact = new int[1_000_001];

	static TreeMap<int[], Integer> divCostInd = new TreeMap<>(COMP_ARR);

	public static void main(String[] args) throws IOException {
		cGen = new int[23];
		numD = new int[6000];
		states = new int[6000][];
		genAll(0, 23, 23, 1);

		aList = new ArrayList[6000];
		for (int i = 0; i < 6000; i++) {
			aList[i] = new ArrayList<>();
		}
		fAList();

		divCost = new int[400][301];
		for (int[] a : divCost) {
			Arrays.fill(a, Integer.MAX_VALUE / 2);
		}
		cost = new int[index.size()];

		Arrays.fill(pFact, 1);
		for (int i = 2; i <= 1_000_000; i++) {
			if (pFact[i] == 1) {
				for (int m = i; m <= 1_000_000; m += i) {
					pFact[m] = i;
				}
			}
		}

		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter printer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));

		int nT = Integer.parseInt(reader.readLine());

		while (nT-- > 0) {
			StringTokenizer inputData = new StringTokenizer(reader.readLine());
			int a = Integer.parseInt(inputData.nextToken());
			int b = Integer.parseInt(inputData.nextToken());

			int[] aA = toArray(a);
			int[] bA = toArray(b);

			Integer aRes = divCostInd.get(aA);
			if (aRes == null) {
				aRes = divCostInd.size();
				bfs(aA, divCostInd.size());
				divCostInd.put(aA, divCostInd.size());
			}
			Integer bRes = divCostInd.get(bA);
			if (bRes == null) {
				bRes = divCostInd.size();
				bfs(bA, divCostInd.size());
				divCostInd.put(bA, divCostInd.size());
			}

			int minA = Integer.MAX_VALUE / 4;
			for (int nD = 1; nD <= 300; nD++) {
				minA = Math.min(minA, divCost[aRes][nD] + divCost[bRes][nD]);
			}
			printer.println(minA);
		}
		printer.close();
	}

	static int[] toArray(int a) {
		ArrayList<Integer> cnts = new ArrayList<Integer>();
		int last = -1;
		int cCnt = 0;

		while (a > 1) {
			int cPFact = pFact[a];
			if (cPFact == last) {
				cCnt++;
			} else {
				if (cCnt != 0) {
					cnts.add(cCnt);
				}
				last = cPFact;
				cCnt = 1;
			}
			a /= pFact[a];
		}
		if (cCnt != 0) {
			cnts.add(cCnt);
		}
		Collections.sort(cnts, Comparator.reverseOrder());
		int[] res = new int[cnts.size()];
		for (int i = 0; i < cnts.size(); i++) {
			res[i] = cnts.get(i);
		}
		return res;
	}

	static int[] cost;

	static int[][] divCost;

	static void bfs(int[] sState, int searchI) {
		int sInd = index.get(sState);
		ArrayDeque<Integer> queue = new ArrayDeque<>();

		queue.add(index.get(sState));

		Arrays.fill(cost, -1);
		cost[sInd] = 0;

		while (!queue.isEmpty()) {
			int cStInd = queue.remove();
			for (int nStInd : aList[cStInd]) {
				if (cost[nStInd] == -1) {
					cost[nStInd] = cost[cStInd] + 1;
					queue.add(nStInd);
				}
			}
		}

		for (Entry<int[], Integer> cE : index.entrySet()) {
			int cNumD = numD[cE.getValue()];
			if (cNumD <= 300) {
				divCost[searchI][cNumD] = Math.min(divCost[searchI][cNumD], cost[cE.getValue()]);
			}
		}
	}

	static ArrayList<Integer>[] aList;

	static void fAList() {
		int[] cState = new int[32];
		for (Entry<int[], Integer> cE : index.entrySet()) {
			int[] oState = cE.getKey();
			int cStInd = cE.getValue();

			int cLen = states[cStInd].length;
			for (int i = 0; i < cLen; i++) {
				cState[i] = oState[i];
			}
			MODE = cLen;

			for (int i = 0; i < cLen; i++) {
				if (i == 0 || cState[i - 1] > cState[i]) {
					cState[i]++;
					Integer nStInd = index.get(cState);
					cState[i]--;

					if (nStInd == null) {
						continue;
					}
					aList[cStInd].add(nStInd);
				}

				if (i == cLen - 1 && cState[i] == 1) {
					MODE--;
					Integer nStInd = index.get(cState);
					MODE++;
					if (nStInd == null) {
						continue;
					}
					aList[cStInd].add(nStInd);
				} else if (i == cLen - 1 || cState[i] > cState[i + 1]) {
					cState[i]--;
					Integer nStInd = index.get(cState);
					cState[i]++;
					if (nStInd == null) {
						continue;
					}
					aList[cStInd].add(nStInd);
				}
			}
			cState[cLen] = 1;

			MODE++;
			Integer nStInd = index.get(cState);
			MODE--;
			if (nStInd == null) {
				continue;
			}
			aList[cStInd].add(nStInd);
		}
	}

	static int[] cGen;

	static void genAll(int i, int max, int rem, int cProd) {
		numD[index.size()] = cProd;

		int[] cKey = Arrays.copyOf(cGen, i);
		states[index.size()] = cKey;
		index.put(cKey, index.size());

		if (rem > 0) {
			for (int nV = Math.min(max, rem); nV >= 1; nV--) {
				cGen[i] = nV;
				genAll(i + 1, nV, rem - nV, cProd * (nV + 1));
			}
		}
	}
}