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.

import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;

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

    }

    private static String solve(int n, int[] a) {
        /* Important observations:
         *  An element a[i] can shift iff operation is performed at left side of
         *  that element.
         *  For the given condition to be correct, an element must not be divided by
         *  at least one of indices from 2 to i+1 .
         *  It means that an element must not be divided by all its indices to the left,
         *  otherwise the solution doesn't exists.
         *  This can be achieved by checking if an element is divided by
         *  LCM of all elements ranging from 2  to i+1 .
         * */

        int lcm = 1;
        for (int i = 0; i < n; i++)
        {
            lcm = (lcm * (i + 2)) / gcd(lcm, (i + 2));

            // Check, if it is divided by all its indices to the left or not
            if( a[i]% lcm == 0)
                return "NO";
        }

        return "YES";
    }

    public static void main(String[] args)
            throws IOException {

        Scanner s = new Scanner();
        int t = 1;
        t = s.nextInt();
        StringBuilder ans = new StringBuilder();
        int count = 0;
        while (t-- > 0) {
            int n = s.nextInt();
            int a[] = new int[n];
            getInputs(s, a, n);
            ans.append(solve(n, a)).append("\n");
        }
        System.out.println(ans.toString());
    }

    static class Scanner {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Scanner() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Scanner(String file_name) throws IOException {
            din = new DataInputStream(
                    new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n') {
                    if (cnt != 0) {
                        break;
                    } else {
                        continue;
                    }
                }
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0,
                    BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }

    public static long norm(long a, long MOD) {
        return ((a % MOD) + MOD) % MOD;
    }

    public static long msub(long a, long b, long MOD) {
        return norm(norm(a, MOD) - norm(b, MOD), MOD);

    }

    public static long madd(long a, long b, long MOD) {
        return norm(norm(a, MOD) + norm(b, MOD), MOD);

    }

    public static long mMul(long a, long b, long MOD) {
        return norm(norm(a, MOD) * norm(b, MOD), MOD);


    }

    public static long mDiv(long a, long b, long MOD) {
        return norm(norm(a, MOD) / norm(b, MOD), MOD);
    }

    public static String formattedArray(int a[]) {
        StringBuilder res = new StringBuilder("");
        for (int e : a)
            res.append(e).append(" ");
        return res.toString().trim();

    }

    private static void getInputs(Scanner s, int[] a, int n) throws IOException {
        for (int i = 0; i < n; i++) {
            a[i] = s.nextInt();
        }
    }
}
