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".
import java.util.*;
import java.lang.*;
import java.math.*;
import java.io.*;
 
/* spar5h */

public class cf4 implements Runnable{    
	
	final static long mod = (long)1e9 + 7; 
	
	public void run() {
		
		InputReader s = new InputReader(System.in);
		PrintWriter w = new PrintWriter(System.out);
		
		HashMap<String, Integer> hm = new HashMap<String, Integer>();
		
		String str = s.next(); int n = str.length();
	
		ArrayList<Integer> list = new ArrayList<Integer>();
		
		for(int i = 1; i * i <= n; i++) {
			
			if(n % i != 0)
				continue;
			
			list.add(i);
			
			if(i != n / i)
				list.add(n / i);
		}
		
		for(int i = 0; i < list.size(); i++) {
			
			int k = list.get(i);
			
			String key = str.substring(0, k);
			
			boolean b = true;
			
			for(int j = k; j < n; j += k) {
				
				if(!key.equals(str.substring(j, j + k))) {
					b = false; break;
				}
			}
			
			if(b)
				hm.put(key, hm.get(key) != null ? hm.get(key) + 1 : 1);
		}
		
		str = s.next(); n = str.length();
	
		list = new ArrayList<Integer>();
		
		for(int i = 1; i * i <= n; i++) {
			
			if(n % i != 0)
				continue;
			
			list.add(i);
			
			if(i != n / i)
				list.add(n / i);
		}
		
		for(int i = 0; i < list.size(); i++) {
			
			int k = list.get(i);
			
			String key = str.substring(0, k);
			
			boolean b = true;
			
			for(int j = k; j < n; j += k) {
				
				if(!key.equals(str.substring(j, j + k))) {
					b = false; break;
				}
			}
			
			if(b)
				hm.put(key, hm.get(key) != null ? hm.get(key) + 1 : 1);
		}
		
		int res = 0;
		
		for(int i : hm.values())
			if(i == 2)
				res++;
		
		
		w.println(res);
		w.close();
	}
	
	static class InputReader {
		
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;
		
		public InputReader(InputStream stream)
		{
			this.stream = stream;
		}
		
		public int read()
		{
			if (numChars==-1) 
				throw new InputMismatchException();
			
			if (curChar >= numChars)
			{
				curChar = 0;
				try 
				{
					numChars = stream.read(buf);
				}
				catch (IOException e)
				{
					throw new InputMismatchException();
				}
				
				if(numChars <= 0)				
					return -1;
			}
			return buf[curChar++];
		}
	 
		public String nextLine()
		{
			BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
			String str = "";
        try
        {
            str = br.readLine();
        }
        catch (IOException e)
        {
            e.printStackTrace();
        }
        return str;
	}
	public int nextInt()
	{
		int c = read();
		
		while(isSpaceChar(c)) 
			c = read();
		
		int sgn = 1;
		
		if (c == '-') 
		{
			sgn = -1;
			c = read();
		}
		
		int res = 0;
		do 
		{
			if(c<'0'||c>'9') 
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		}
		while (!isSpaceChar(c)); 
		
		return res * sgn;
	}
	
	public long nextLong() 
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') 
		{
			sgn = -1;
			c = read();
		}
		long res = 0;
		
		do 
		{
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		}
		while (!isSpaceChar(c));
			return res * sgn;
	}
	
	public double nextDouble() 
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') 
		{
			sgn = -1;
			c = read();
		}
		double res = 0;
		while (!isSpaceChar(c) && c != '.') 
		{
			if (c == 'e' || c == 'E')
				return res * Math.pow(10, nextInt());
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		}
		if (c == '.') 
		{
			c = read();
			double m = 1;
			while (!isSpaceChar(c)) 
			{
				if (c == 'e' || c == 'E')
					return res * Math.pow(10, nextInt());
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				m /= 10;
				res += (c - '0') * m;
				c = read();
			}
		}
		return res * sgn;
	}
	
	public String readString() 
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do 
		{
			res.appendCodePoint(c);
			c = read();
		} 
		while (!isSpaceChar(c));
		
		return res.toString();
	}
 
	public boolean isSpaceChar(int c) 
	{
		if (filter != null)
			return filter.isSpaceChar(c);
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}
 
	public String next() 
	{
		return readString();
	}
	
	public interface SpaceCharFilter 
	{
		public boolean isSpaceChar(int ch);
	}
}

public static void main(String args[]) throws Exception
{
	new Thread(null, new cf4(),"cf4",1<<26).start();
	}
}   