Problem: There are n cities in the Kingdom of Autumn, numbered from 1 to n. People can travel between any two cities using n-1 two-directional roads.

This year, the government decides to separate the kingdom. There will be regions of different levels. The whole kingdom will be the region of level 1. Each region of i-th level should be separated into several (at least two) regions of i+1-th level, unless i-th level is the last level. Each city should belong to exactly one region of each level and for any two cities in the same region, it should be possible to travel between them passing the cities in the same region only.

According to research, for each city i, there is a value a_i, which describes the importance of this city. All regions of the same level should have an equal sum of city importances.

Your task is to find how many plans there are to determine the separation of the regions that all the conditions are satisfied. Two plans are considered different if and only if their numbers of levels are different or there exist two cities in the same region of one level in one plan but in different regions of this level in the other plan. Since the answer may be very large, output it modulo 10^9+7.

Input

The first line contains one integer n (1 ≤ n ≤ 10^6) — the number of the cities.

The second line contains n integers, the i-th of which is a_i (1 ≤ a_i ≤ 10^9) — the value of each city.

The third line contains n-1 integers, p_1, p_2, …, p_{n-1}; p_i (p_i ≤ i) describes a road between cities p_i and i+1.

Output

Print one integer — the number of different plans modulo 10^9+7.

Examples

Input

4
1 1 1 1
1 2 3


Output

4

Input

4
1 1 1 1
1 2 2


Output

2

Input

4
1 2 1 2
1 1 3


Output

3

Note

For the first example, there are 4 different plans:

Plan 1: Level-1: \{1,2,3,4\}.

Plan 2: Level-1: \{1,2,3,4\}, Level-2: \{1,2\},\{3,4\}.

Plan 3: Level-1: \{1,2,3,4\}, Level-2: \{1\},\{2\},\{3\},\{4\}.

Plan 4: Level-1: \{1,2,3,4\}, Level-2: \{1,2\},\{3,4\}, Level-3: \{1\},\{2\},\{3\},\{4\}.

For the second example, there are 2 different plans:

Plan 1: Level-1: \{1,2,3,4\}.

Plan 2: Level-1: \{1,2,3,4\}, Level-2: \{1\},\{2\},\{3\},\{4\}.

For the third example, there are 3 different plans:

Plan 1: Level-1: \{1,2,3,4\}.

Plan 2: Level-1: \{1,2,3,4\}, Level-2: \{1,2\},\{3,4\}.

Plan 3: Level-1: \{1,2,3,4\}, Level-2: \{1,3\},\{2\},\{4\}.

Solution (in JAVA):

Solution:
import java.lang.*;
import java.math.*;
import java.util.*;
import java.io.*;

public class Main {

    void solve(){
        int n=ni();
        val=new long[n+1];
        for(int i=1;i<=n;i++) val[i]=nl();

        int from[]=new int[n-1];
        int to[]=new int[n-1];
       g=new int[n+1][];
        for(int i=1;i<n;i++){
            int p=ni();
            from[i-1]=p; to[i-1]=i+1;
        }
        g=packU(n,from,to);
        dfs(1,-1);
        long S=val[1];
        int cnt[]=new int[n+1];
        for(int i=1;i<=n;i++) val[i]=S/gcd(val[i],S);
        for(int i=1;i<=n;i++){
            if(val[i]<=n) cnt[(int)val[i]]++;
        }
        for(int i=n;i>0;i--) for(int j=2*i;j<=n;j+=i) cnt[j]+=cnt[i];
        int dp[]=new int[n+1];

        int div[][]=new int[n+1][];
        int cc[]=new int[n+1];
        for(int i=1;i<=n;i++){
            for(int j=2*i;j<=n;j+=i) cc[j]++;
        }
        for(int i=1;i<=n;i++) div[i]=new int[cc[i]];
        Arrays.fill(cc,0);
        for(int i=1;i<=n;i++){
            for(int j=2*i;j<=n;j+=i) div[j][cc[j]++]=i;
        }

        dp[1]=1;
        for(int i=2;i<=n;i++){
            if(cnt[i]==i){
                for(int j : div[i]) {
                    dp[i]+=dp[j];
                    if(dp[i]>=M) dp[i]-=M;
                }
            }
        }
        long ans=0;
        for(int i=1;i<=n;i++) if(cnt[i]==i) { ans+=dp[i]; if(ans>=M) ans-=M; }
        pw.println(ans);
    }
    long val[];
   int g[][];

    void dfs(int v,int pr){
        for(int u : g[v]){
            if(u!=pr){
                dfs(u,v);
                val[v]+=val[u];
            }
        }
    }
    long gcd(long a,long b){
        long r;
        while(b!=0){
            r=a%b;
            a=b;
            b=r;
        }
        return a;
    }

    static int[][] packU(int n, int[] from, int[] to) {
        int[][] g = new int[n+1][];
        int[] p = new int[n+1];
        for (int f : from)
            p[f]++;
        for (int t : to)
            p[t]++;
        for (int i = 1; i <= n; i++)
            g[i] = new int[p[i]];
        for (int i = 0; i < from.length; i++) {
            g[from[i]][--p[from[i]]] = to[i];
            g[to[i]][--p[to[i]]] = from[i];
        }
        return g;
    }




    long M= (long)1e9+7;
    InputStream is;
    PrintWriter pw;
    String INPUT = "";
    void run() throws Exception {
        is = is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        pw = new PrintWriter(System.out);

        Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){
            @Override
            public void run() {
                long s = System.currentTimeMillis();
                solve();

                pw.flush();
                if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
            }
        };
        t.start();
        t.join();
    }
    public static void main(String[] args) throws Exception { new Main().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 = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }

    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(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(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(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 && !(isSpaceChar(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(INPUT.length() > 0)System.out.println(Arrays.deepToString(o)); }

}