Vasya has recently learned at school what a number's divisor is and decided to determine a string's divisor. Here is what he came up with.

String a is the divisor of string b if and only if there exists a positive integer x such that if we write out string a consecutively x times, we get string b. For example, string "abab" has two divisors — "ab" and "abab".

Now Vasya wants to write a program that calculates the number of common divisors of two strings. Please help him.

Input

The first input line contains a non-empty string s1.

The second input line contains a non-empty string s2.

Lengths of strings s1 and s2 are positive and do not exceed 105. The strings only consist of lowercase Latin letters.

Output

Print the number of common divisors of strings s1 and s2. 

Examples

Input

abcdabcd
abcdabcdabcdabcd


Output

2


Input

aaa
aa


Output

1

Note

In first sample the common divisors are strings "abcd" and "abcdabcd".

In the second sample the common divisor is a single string "a". String "aa" isn't included in the answer as it isn't a divisor of string "aaa".
/*
 * Author Ayub Subhaniya
 * Institute DA-IICT
 */

import java.io.*;
import java.math.*;
import java.util.*;


public class B{
	
	InputStream in;
	PrintWriter out;
	
	
	void solve() {
		String s1=ns();
		String s2=ns();
		Hash h1=new Hash(s1);
		Hash h2=new Hash(s2);
		int max=Math.min(s1.length(), s2.length());
		long hash;
		boolean flag;
		int cnt=0;
		//tr(max);
		for (int i=1;i<=max;i++)
		{
			//tr(i+"***");
			if (s1.length()%i!=0||s2.length()%i!=0)
				continue;
			
			hash=h1.getHash1(1, 1+i-1);
			flag=true;
			for (int j=i;(i+j-1)<s1.length();j+=i)
			{
				if (hash!=h1.getHash1(j+1, j+i))
				{
					//tr(j);
					flag=false;
					break;
				}
			}
			
			if (!flag)
				continue;
			
			for (int j=0;(i+j-1)<s2.length();j+=i)
			{
				if (hash!=h2.getHash1(j+1, j+i))
				{
					//tr(j);
					flag=false;
					break;
				}
			}
			
			if (flag)
				{
					cnt++;
				}
		}
		out.println(cnt);
	}
	
	class Hash {
		long hash1[];
		long MOD = 1000000007;
		int MAX = 100005;
		long power[] = new long[MAX + 1];
		long inverse1[] = new long[MAX + 1];

		Hash(String s) {
			power();
			hash1 = new long[s.length() + 1];

			hash1[1] = (s.charAt(0) - 'a');
			for (int i = 2; i <= s.length(); i++) {
				hash1[i] = (hash1[i - 1] + ((s.charAt(i - 1) - 'a') * power[i - 1]) % MOD) % MOD;
			}

		}

		void power() {
			power[0] = 1;

			inverse1[0] = modInverse(power[0], MOD);
			long inv=modInverse(29, MOD);
			for (int i = 1; i < MAX; i++) {
				power[i] = (power[i - 1] * 29) % MOD;
				inverse1[i] = (inverse1[i-1]*inv)%MOD;
			}
		}

		long modInverse(long A, long M) {
			extendedEuclid(A, M);
			return (x % M + M) % M;
		}

		long d, x, y;

		void extendedEuclid(long A, long B) {
			if (B == 0) {
				d = A;
				x = 1;
				y = 0;
			} else {
				extendedEuclid(B, A % B);
				long temp = x;
				x = y;
				y = temp - (A / B) * y;
			}
		}

		long getHash1(int l, int r) {
			long h = (((hash1[r] - hash1[l - 1]) % MOD + MOD) * inverse1[l]) % MOD;
			return h;
		}

	}
	
	void run() throws Exception {
		String INPUT = "C:/Users/ayubs/Desktop/input.txt";
		in = oj ? System.in : new FileInputStream(INPUT);
		out = new PrintWriter(System.out);
		
			long s = System.currentTimeMillis();
			solve();
			out.flush();
			tr(System.currentTimeMillis() - s + "ms");
	}
	public static void main(String[] args) throws Exception {
		new B().run();
	}
	
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	
	private int readByte() {
		if (lenbuf == -1)
			throw new InputMismatchException();
		if (ptrbuf >= lenbuf) {
			ptrbuf = 0;
			try {
				lenbuf = in.read(inbuf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (lenbuf <= 0)
				return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean inSpaceChar(int c) {
		return !(c >= 33 && c <= 126);
	}
	
	private int skip() {
		int b;
		while ((b = readByte()) != -1 && inSpaceChar(b))
			;
		return b;
	}
	
	private double nd() {
		return Double.parseDouble(ns());
	}
	
	private char nc() {
		return (char) skip();
	}
	
	private String ns() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!(inSpaceChar(b))) { // when nextLine, (inSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n) {
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while (p < n && !(inSpaceChar(b))) {
			buf[p++] = (char) b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for (int i = 0; i < n; i++)
			map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}
	
	private int ni() {
		int num = 0, b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		
		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl() {
		long num = 0;
		int b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		
		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	
	private void tr(Object... o) {
		if (!oj)
			System.out.println(Arrays.deepToString(o));
	}
	
}
