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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.text.DecimalFormat;
import java.util.*;
import java.util.concurrent.ThreadLocalRandom;
import java.util.stream.Collectors;
import java.util.stream.IntStream;
import java.util.stream.LongStream;

public class TaskB {

    static long mod = 1000000007;
    static FastScanner scanner;

    static final StringBuilder result = new StringBuilder();

    public static void main(String[] args) {
        scanner = new FastScanner();
        int T = scanner.nextInt();
        for (int t = 0; t < T; t++) {
            solve();
            result.append("\n");
        }
        System.out.println(result);
    }

    static void solve() {
        int n = scanner.nextInt();
        int[] a = scanner.nextIntArray(n);
        int removed = 0;
        for (int i = 0; i < n; i++) {
            boolean canBeRemoved = false;
            for (int j = 0; j <= i; j++) {
                if (a[i] % (i + 2 - j) != 0) {
                    canBeRemoved = true;
                    break;
                }
            }
            if (!canBeRemoved) {
                result.append("NO");
                return;
            }
        }
        result.append("YES");
    }

    static class WithIdx implements Comparable<WithIdx> {
        int val, idx;

        public WithIdx(int val, int idx) {
            this.val = val;
            this.idx = idx;
        }

        @Override
        public int compareTo(WithIdx o) {
            if (val == o.val) {
                return Integer.compare(idx, o.idx);
            }
            return Integer.compare(val, o.val);
        }
    }

    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

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

        String nextToken() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    // TODO Auto-generated catch block
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        String nextLine() {
            try {
                return br.readLine();
            } catch (Exception e) {
                e.printStackTrace();
                throw new RuntimeException();
            }
        }

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

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

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

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

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

        String[] nextStringArray(int n) {
            String[] res = new String[n];
            for (int i = 0; i < n; i++) res[i] = nextToken();
            return res;
        }
    }

    static class PrefixSums {
        long[] sums;

        public PrefixSums(long[] sums) {
            this.sums = sums;
        }

        public long sum(int fromInclusive, int toExclusive) {
            if (fromInclusive > toExclusive) throw new IllegalArgumentException("Wrong value");
            return sums[toExclusive] - sums[fromInclusive];
        }

        public static PrefixSums of(int[] ar) {
            long[] sums = new long[ar.length + 1];
            for (int i = 1; i <= ar.length; i++) {
                sums[i] = sums[i - 1] + ar[i - 1];
            }
            return new PrefixSums(sums);
        }

        public static PrefixSums of(long[] ar) {
            long[] sums = new long[ar.length + 1];
            for (int i = 1; i <= ar.length; i++) {
                sums[i] = sums[i - 1] + ar[i - 1];
            }
            return new PrefixSums(sums);
        }
    }

    static class ADUtils {
        static void sort(int[] ar) {
            Random rnd = ThreadLocalRandom.current();
            for (int i = ar.length - 1; i > 0; i--) {
                int index = rnd.nextInt(i + 1);
                // Simple swap
                int a = ar[index];
                ar[index] = ar[i];
                ar[i] = a;
            }
            Arrays.sort(ar);
        }

        static void reverse(int[] arr) {
            int last = arr.length / 2;
            for (int i = 0; i < last; i++) {
                int tmp = arr[i];
                arr[i] = arr[arr.length - 1 - i];
                arr[arr.length - 1 - i] = tmp;
            }
        }

        static void sort(long[] ar) {
            Random rnd = ThreadLocalRandom.current();
            for (int i = ar.length - 1; i > 0; i--) {
                int index = rnd.nextInt(i + 1);
                // Simple swap
                long a = ar[index];
                ar[index] = ar[i];
                ar[i] = a;
            }
            Arrays.sort(ar);
        }
    }

    static class MathUtils {
        static long[] FIRST_PRIMES = {
                2, 3, 5, 7, 11, 13, 17, 19, 23, 29,
                31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
                73, 79, 83, 89, 97, 101, 103, 107, 109, 113,
                127, 131, 137, 139, 149, 151, 157, 163, 167, 173,
                179, 181, 191, 193, 197, 199, 211, 223, 227, 229,
                233, 239, 241, 251, 257, 263, 269, 271, 277, 281,
                283, 293, 307, 311, 313, 317, 331, 337, 347, 349,
                353, 359, 367, 373, 379, 383, 389, 397, 401, 409,
                419, 421, 431, 433, 439, 443, 449, 457, 461, 463,
                467, 479, 487, 491, 499, 503, 509, 521, 523, 541,
                547, 557, 563, 569, 571, 577, 587, 593, 599, 601,
                607, 613, 617, 619, 631, 641, 643, 647, 653, 659,
                661, 673, 677, 683, 691, 701, 709, 719, 727, 733,
                739, 743, 751, 757, 761, 769, 773, 787, 797, 809,
                811, 821, 823, 827, 829, 839, 853, 857, 859, 863,
                877, 881, 883, 887, 907, 911, 919, 929, 937, 941,
                947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013,
                1019, 1021, 1031, 1033, 1039, 1049, 1051};

        static long[] primes(int to) {
            long[] all = new long[to + 1];
            long[] primes = new long[to + 1];
            all[1] = 1;
            int primesLength = 0;
            for (int i = 2; i <= to; i++) {
                if (all[i] == 0) {
                    primes[primesLength++] = i;
                    all[i] = i;
                }
                for (int j = 0; j < primesLength && i * primes[j] <= to && all[i] >= primes[j];
                        j++) {
                    all[(int) (i * primes[j])] = primes[j];
                }
            }
            return Arrays.copyOf(primes, primesLength);
        }

        static long modpow(long b, long e, long m) {
            long result = 1;

            while (e > 0) {
                if ((e & 1) == 1) {
                    /* multiply in this bit's contribution while using modulus to keep
                     * result small */
                    result = (result * b) % m;
                }
                b = (b * b) % m;
                e >>= 1;
            }

            return result;
        }

        static long submod(long x, long y, long m) {
            return (x - y + m) % m;
        }

        static long modInverse(long a, long m) {
            long g = gcdF(a, m);
            if (g != 1) {
                throw new IllegalArgumentException("Inverse doesn't exist");
            } else {
                // If a and m are relatively prime, then modulo
                // inverse is a^(m-2) mode m
                return modpow(a, m - 2, m);
            }
        }

        static public long gcdF(long a, long b) {
            while (b != 0) {
                long na = b;
                long nb = a % b;
                a = na;
                b = nb;
            }
            return a;
        }
    }
}

/*
5
3 2 3 8 8
2 8 5 10 1

 */