Dima the hamster enjoys nibbling different things: cages, sticks, bad problemsetters and even trees!

Recently he found a binary search tree and instinctively nibbled all of its edges, hence messing up the vertices. Dima knows that if Andrew, who has been thoroughly assembling the tree for a long time, comes home and sees his creation demolished, he'll get extremely upset. 

To not let that happen, Dima has to recover the binary search tree. Luckily, he noticed that any two vertices connected by a direct edge had their greatest common divisor value exceed 1.

Help Dima construct such a binary search tree or determine that it's impossible. The definition and properties of a binary search tree can be found [here.](https://en.wikipedia.org/wiki/Binary_search_tree)

Input

The first line contains the number of vertices n (2 ≤ n ≤ 700).

The second line features n distinct integers a_i (2 ≤ a_i ≤ 10^9) — the values of vertices in ascending order.

Output

If it is possible to reassemble the binary search tree, such that the greatest common divisor of any two vertices connected by the edge is greater than 1, print "Yes" (quotes for clarity).

Otherwise, print "No" (quotes for clarity).

Examples

Input

6
3 6 9 18 36 108


Output

Yes


Input

2
7 17


Output

No


Input

9
4 8 10 12 15 18 33 44 81


Output

Yes

Note

The picture below illustrates one of the possible trees for the first example.

<image>

The picture below illustrates one of the possible trees for the third example.

<image>
//package Contest505;

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Scanner;

public class Main505D {
    public static Scanner enter = new Scanner(System.in);
    public static long millis = 0;
    public static void main(String[] args) throws Exception {
       new Main505D().run();
        //System.out.println(System.currentTimeMillis()-millis);
    }
    public static boolean func (int a,int b){

        while (b !=0) {
            int tmp = a%b;
            a = b;
            b = tmp;
        }
        return a!=1;
    }
    public static boolean[][] arr;
    public  void solve(){
        int n=ni();
        arr=new boolean[n][n];
        boolean[][] dp1= new boolean[n][n];
        boolean[][] dp2= new boolean[n][n];
        int[] mass = new int[n];
        for (int i = 0; i <n ; i++) {
            mass[i]=ni();
        }
        millis = System.currentTimeMillis();
        for (int i = 0; i <n ; i++) {
            for (int j = i+1; j <n ; j++) {
                arr[i][j]=func(mass[i],mass[j]);
            }
        }
        dp1[n-1][n-1]=true;
        dp2[n-1][n-1]=true;
        for (int l = n-2; l>=0 ; l--) {
            dp1[l][l]=true;
            dp2[l][l]=true;
            for (int r = l+1; r <=n-1 ; r++) {
                for (int i = 1; i <=r-l ; i++) {
                    dp1[l][r]|=arr[l][l+i]&&dp1[l+i][r]&&dp2[l+1][l+i];
                    dp2[l][r]|=arr[r-i][r]&&dp1[r-i][r-1]&&dp2[l][r-i];
                }
            }
        }

        boolean answer=false;
        for (int i = 0; i <n ; i++) {
            answer|=dp2[0][i]&&dp1[i][n-1];
            // System.out.println(dp2[0][i] +" "+dp1[i][n-1]);
        }
        pw.println(answer? "Yes": "No");
    }


    long M=(long)1e9+7;
    InputStream is;
    PrintWriter pw;
    String INPUT = "";
    void run() throws Exception {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        pw = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
        solve();
        pw.flush();
        if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");

    }


    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)); }
}
