YouKn0wWho has an integer sequence a_1, a_2, …, a_n. He will perform the following operation until the sequence becomes empty: select an index i such that 1 ≤ i ≤ |a| and a_i is not divisible by (i + 1), and erase this element from the sequence. Here |a| is the length of sequence a at the moment of operation. Note that the sequence a changes and the next operation is performed on this changed sequence.

For example, if a=[3,5,4,5], then he can select i = 2, because a_2 = 5 is not divisible by i+1 = 3. After this operation the sequence is [3,4,5].

Help YouKn0wWho determine if it is possible to erase the whole sequence using the aforementioned operation.

Input

The first line contains a single integer t (1 ≤ t ≤ 10 000) — the number of test cases.

The first line of each test case contains a single integer n (1 ≤ n ≤ 10^5).

The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9).

It is guaranteed that the sum of n over all test cases doesn't exceed 3 ⋅ 10^5.

Output

For each test case, print "YES" (without quotes) if it is possible to erase the whole sequence using the aforementioned operation, print "NO" (without quotes) otherwise. You can print each letter in any register (upper or lower).

Example

Input


5
3
1 2 3
1
2
2
7 7
10
384836991 191890310 576823355 782177068 404011431 818008580 954291757 160449218 155374934 840594328
8
6 69 696 69696 696969 6969696 69696969 696969696


Output


YES
NO
YES
YES
NO

Note

In the first test case, YouKn0wWho can perform the following operations (the erased elements are underlined): [1, \underline{2}, 3] → [\underline{1}, 3] → [\underline{3}] → [ ].

In the second test case, it is impossible to erase the sequence as i can only be 1, and when i=1, a_1 = 2 is divisible by i + 1 = 2.
// HOPE

////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
//----------------------------------------------------------------------------------------------------------------------
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
//----------------------------------------------------------------------------------------------------------------------
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
///////                                                                                                       //////////
///////                                                                                                       //////////
///////            RRRRRRRRRRRRR     YY          YY         AA               NN         NN                    //////////
///////            RR         RR      YY        YY        AA  AA             NN NN      NN                    //////////
///////            RR        RR         YY     YY        AA    AA            NN  NN     NN                    //////////
///////            RRRRRRRRRR            YY   YY       AAAAAAAAAAAA          NN    NN   NN                    //////////
///////            RR RR                   YY         AAAAAAAAAAAAAA         NN      NN NN                    //////////
///////            RR   RR                 YY        AA            AA        NN       NNNN                    //////////
///////            RR     RR               YY       AA              AA       NN         NN                    //////////
///////            RR       RR_____________________________________________________________________________   //////////
////////                                                                                                      //////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
//----------------------------------------------------------------------------------------------------------------------
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
//----------------------------------------------------------------------------------------------------------------------
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////


import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Codeforces2 {
    static PrintWriter out = new PrintWriter(System.out);
    static final int mod=1_000_000_007;

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

        int[] readIntArray(int n){
            int[] a = new int[n];
            for(int i=0;i<n;i++)
                a[i] = nextInt();
            return a;
        }

        long[] readLongArray(int n){
            long[] a = new long[n];
            for(int i=0;i<n;i++)
                a[i] = nextLong();
            return a;
        }

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    //Try seeing general case
    public static void main(String[] args) {
        FastReader s = new FastReader();
        int t = s.nextInt();
        while(t-->0)
        {
            int n = s.nextInt();
            long[] a = s.readLongArray(n);
            out.println(find(n, a));
        }

        out.close();
    }

    public static String find(int n, long[] a)
    {
        if(a[0]%2==0)
            return "NO";

        int val = 0;
        boolean fine;
        for(int i=0;i<n;i++)
        {
            int index = i+2;
            if(a[i]%index!=0)
            {
                val++;
            }
            else
            {
                fine = false;
                for(int j=1;j<=val;j++)
                {
                    if (a[i] % (index - j) != 0)
                    {
                        fine = true;
                        val++;
                        break;
                    }
                }
                if(!fine)
                    return "NO";
            }
        }
        return "YES";
    }





















































    /////////////////////////////////////////////////THE END///////////////////////////////////////////////////////////
    //////////////////////////////////////////////////////////////////////////////////////////////////////////////////

    public static int gcd(int x,int y)
    {
        return y==0?x:gcd(y,x%y);
    }
    public static long gcd(long x,long y)
    {
        return y==0L?x:gcd(y,x%y);
    }

    public static int lcm(int a, int b) {
        return (a * b) / gcd(a, b);
    }
    public static long lcm(long a, long b) {
        return (a * b) / gcd(a, b);
    }

    public static long pow(long a,long b)
    {
        if(b==0L)
            return 1L;
        long tmp=1;
        while(b>1L)
        {
            if((b&1L)==1)
                tmp*=a;
            a*=a;
            b>>=1;
        }
        return (tmp*a);
    }

    public static long modPow(long a,long b,long mod)
    {
        if(b==0L)
            return 1L;
        long tmp=1;
        while(b>1L)
        {
            if((b&1L)==1L)
                tmp*=a;

            a*=a;
            a%=mod;
            tmp%=mod;
            b>>=1;
        }
        return (tmp*a)%mod;
    }

    static long mul(long a, long b) {
        return a*b%mod;
    }

    static long fact(int n) {
        long ans=1;
        for (int i=2; i<=n; i++) ans=mul(ans, i);
        return ans;
    }

    static long fastPow(long base, long exp) {
        if (exp==0) return 1;
        long half=fastPow(base, exp/2);
        if (exp%2==0) return mul(half, half);
        return mul(half, mul(half, base));
    }

    static void debug(int ...a)
    {
        for(int x: a)
            out.print(x+" ");
        out.println();
    }

    static void debug(long ...a)
    {
        for(long x: a)
            out.print(x+" ");
        out.println();
    }

    static void debugMatrix(int[][] a)
    {
        for(int[] x:a)
            out.println(Arrays.toString(x));
    }
    static void debugMatrix(long[][] a)
    {
        for(long[] x:a)
            out.println(Arrays.toString(x));
    }

    static void reverseArray(int[] a) {
        int n = a.length;
        int[] arr = new int[n];
        for (int i = 0; i < n; i++)
            arr[i] = a[n - i - 1];
        for (int i = 0; i < n; i++)
            a[i] = arr[i];
    }

    static void reverseArray(long[] a) {
        int n = a.length;
        long[] arr = new long[n];
        for (int i = 0; i < n; i++)
            arr[i] = a[n - i - 1];
        for (int i = 0; i < n; i++)
            a[i] = arr[i];
    }

    static void sort(int[] a)
    {
        ArrayList<Integer> ls = new ArrayList<>();
        for(int x: a) ls.add(x);
        Collections.sort(ls);
        for(int i=0;i<a.length;i++)
            a[i] = ls.get(i);
    }

    static class Pair{
        int x, y;
        Pair(int x, int y)
        {
            this.x = x;
            this.y = y;
        }

        @Override
        public String toString() {
            return "Pair{" +
                    "x=" + x +
                    ", y=" + y +
                    '}';
        }
    }
    static class MyCmp implements Comparator<Pair>
    {
        public int compare(Pair p1, Pair p2)
        {
            return p1.x-p2.x;
        }
    }
}
