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.*;
import java.util.Arrays;
import java.util.StringTokenizer;


//start of Scanner class


public class msa {
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static PrintWriter pw = new PrintWriter(System.out);
    static StringTokenizer st;
    static Snner sc = new Snner(System.in);

    static public int maximumProduct(int[] num) {

        int max1 = 1, max2 = 1;
        Arrays.sort(num);
        for (int i = 0; i < 3; i++) {
            max1 *= num[num.length - 1 - i];
            if (i < 2)
                max2 *= num[i];
        }
        max2 *= num[num.length - 1];
        return max1 > max2 ? max1 : max2;
    }

    public static void main(String args[]) throws NumberFormatException, IOException {
        int t = sc.nextInt();
        while (t-- > 0) {
            long arr[] = new long[sc.nextInt()];
            for (int i = 0; i < arr.length; i++) arr[i] = sc.nextLong();
            pw.println(solve_c(arr) ? "yes" : "no");
        }
        pw.close();
    }

    //segtree
    static long b(int arr[][]) {
        int s = 1;
        int e = (int) 10e9;
        int mid;
        while (s <= e) {
            mid = s + ((e - s) >> 1);
            int temp = sum(arr, mid);
            if (temp < 0) s = mid + 1;
            else if (temp == 0) return mid;
            else e = mid - 1;

        }
        return s;
    }

    static long solve(long arr[][]) {
        long b[] = new long[arr.length];
        long max0 = Long.MIN_VALUE;
        for (int i = 0; i < arr.length; i++) {
            long max = Long.MIN_VALUE;
            for (int j = 1; j < arr[i].length; j++) {
                max = Math.max(max, arr[i][j] - j + 1);
            }
            long k = arr[i].length;
            b[i] = max - k;
        }
        Arrays.sort(b);
        return b[b.length - 1];
    }

    private static int sum(int[][] arr, int mid) {
        int sum = arr[0][0] + 1;

        for (int i = 0; i < arr.length; i++) {
            for (int j = 1; j < arr[i].length; j++) {
                if (sum < arr[i][j]) sum += 1 + arr[i][j] - sum;
                sum++;
            }
        }
        return mid - sum;

    }

    static long solveb(long n, long k) {
        ;

        long done = 1;
        long poss = 1;
        long i = 0;
        if (k == 1) return n - 1;
        if (k > n) k = n;
        while (done < k && done < n) {
            i++;
            done += poss;
            poss = done;
        }
        if ((n - done) % k > 0) i++;
        i += (n - done) / k;
        return i;
    }

    //
    //end of public clas
    static String solve_a(String x) {
        int a = 0, b = 0;
        for (int i = 0; i < x.length() - 1; i++) {
            if (x.charAt(i) != x.charAt(i + 1)) {
                if (x.charAt(i) == 'a') a++;
                else b++;
            }
        }
        //char aa[] = x.toCharArray();
        StringBuilder xx = new StringBuilder(x);
        if (a == b) return x;

        else if (a > b) {
            for (int i = 0; i < x.length(); i++) {
                if (x.charAt(i) == 'a') {
                    xx.setCharAt(i, 'b');
                    break;
                }
            }
        } else {
            for (int i = 0; i < x.length(); i++) {
                if (x.charAt(i) == 'b') {
                    xx.setCharAt(i, 'a');
                    break;
                }

            }
        }
        return xx.toString();
    }

    static void solve_c() throws IOException {
        long sum = 0;
        long t = sc.nextLong();
        while (t-- > 0) {

            int n = sc.nextInt();
            long k = sc.nextLong();
            long arr[] = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = (long) Math.pow(10, sc.nextLong());
            }
            int i = 0;
            while (k > 0) {
                arr[n - 1 - (i)] = k / arr[n - 1 - i];
                if (arr[n - 1 - i] != 0)
                    k %= arr[n - 1 - i];
                i++;
            }

            for (long a : arr) sum += a;
            pw.println(sum);
            sum = 0;
        }
    }

    static boolean solve_c(long arr[]) {
        boolean done = true, found = false;
        for (int j = 0; j < arr.length; j++) {
            found = false;
            for (int i = j + 2; i >= 2; i--) {
                if (arr[j] % i != 0) {
                    found = true;
                    break;
                }
            }
            done &= found;
            if (done == false) return false;
        }
        return done;
    }

    int count(String x) {
        int c = 0;
        for (int i = 0; i < x.length() - 1; i++) {
            if (x.charAt(i) != x.charAt(i + 1))
                c++;
        }
        return c;
    }


    boolean prime_or_not(long x) {
        if (x % 2 == 0 || x % 3 == 0) return false;
        for (long i = 6; i * i < x; i += 6)
            if (x % (i + 1) == 0 || x % (i - 1) == 0) return false;

        return true;
    }

    static class Snner {
        StringTokenizer st;
        BufferedReader br;

        public Snner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Snner(FileReader r) {
            br = new BufferedReader(r);
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

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

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

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++)
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec)
                        f *= 10;
                }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }

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

        public Long[] nextLongArray(int n) throws IOException {
            Long[] a = new Long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }

        public int[] nextIntArray(int n) throws IOException {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public Integer[] nextIntegerArray(int n) throws IOException {
            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public boolean ready() throws IOException {
            return br.ready();
        }

    }

    class SegmentTree {
        int N, n;
        long[] arr, a;
        long ident;

        //arr = segment tree;
        //a is input_array but (1 based , its len is completed to power 2 with identity values if possible );
        //N =len of a;
        //n=num of input array element ;
        // All index are 1 based except for am array (in the constructor);

        SegmentTree(long[] am, long ident) {
            n = am.length;
            N = 1;
            while (N < n) N *= 2;

            a = new long[N + 1];
            this.ident = ident;
            Arrays.fill(a, ident);
            for (int i = 0; i < n; i++) a[i + 1] = am[i];

            arr = new long[2 * N];
            Arrays.fill(arr, ident);

            build(1, 1, N);
        }

        long build(int node, int l, int r) {
            if (l == r) return arr[node] = a[node - (N - 1)];
            int mid = (l + r) / 2;
            return arr[node] = build(2 * node, l, mid) + build(2 * node + 1, mid + 1, r);

        }

        void update_point(int index, long new_value) {
            arr[N - 1 + index] = new_value;
            index = index + N - 1;
            while (index > 1) {
                index /= 2;
                arr[index] = arr[2 * index] + arr[2 * index + 1];
            }
        }

        long query(int l, int r) {
            return q(1, 1, N, l, r);

        }

        private long q(int node, int s, int e, int l, int r) {
            if (l > e || r < s) return ident;
            if (s >= l && e <= r) return arr[node];
            int mid = (s + e) / 2;
            return q(node * 2, s, mid, l, r) + q(node * 2 + 1, mid + 1, e, l, r);
        }

    }

}