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.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * 111118315581
 *
 * -3 3 2 3 2 3 2 3 -3 3 -3 3 -3 3 2 3
 *
 * @author pttrung
 */
public class A {

    public static long x, y, gcd;
    public static int Mod = 1000000007;

    public static void main(String[] args) throws FileNotFoundException {
        Scanner in = new Scanner();
        PrintWriter out = new PrintWriter(System.out);
        // PrintWriter out = new PrintWriter(new FileOutputStream(new File("output.txt")));
        String a = in.next();
        String b = in.next();
        int gcd = gcd(a.length(), b.length());
        String comp = null;
        for (int i = 1; i <= gcd; i++) {
            if (gcd % i == 0) {
                comp = getSub(i, a);
                if (comp != null) {
                    break;
                }
            }
        }
        //    System.out.println(comp);
        if (comp != null) {
            String other = getSub(comp.length(), b);
            if (comp.equals(other)) {
                int count = 1;
                int result = 0;
                int l = comp.length();
                int lA = a.length();
                int lB = b.length();
               // System.out.println(lA + " " + lB);
                while (l * count <= lA && l * count <= lB) {
                    if (lA % (l*count) == 0 && lB % (l*count) == 0) {
                        result++;
                    }
                    count++;
                }
                out.println(result);

            } else {
                out.println(0);
            }
        } else {
            out.println(0);
        }

        out.close();
    }

    public static String getSub(int length, String val) {
        String sub = val.substring(0, length);
        for (int i = length; i < val.length(); i += length) {
            String temp = val.substring(i, i + length);
            if (!temp.equals(sub)) {
                return null;
            }
        }
        return sub;
    }

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

    public static void extendEuclid(long a, long b) {
        if (b == 0) {
            x = 1;
            y = 0;
            gcd = a;
            return;
        }
        extendEuclid(b, a % b);
        long x1 = y;
        long y1 = x - (a / b) * y;
        x = x1;
        y = y1;

    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            // System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //      br = new BufferedReader(new InputStreamReader(new FileInputStream(new File("basketball_game.txt"))));
        }

        public String next() {

            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}