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.io.PrintWriter;
import java.util.*;

import static java.lang.Math.abs;
import static java.lang.Math.max;
import static java.lang.System.*;
import static java.util.Arrays.sort;
import static java.util.Collections.replaceAll;
import static java.util.Collections.reverseOrder;

public class C {
    public static final boolean LOCAL = System.getProperty("ONLINE_JUDGE") == null;
    // public static final boolean LOCAL = System.getProperty("LOCAL")!=null;
    public static final String ANSI_RED = "\u001B[31m";
    public static final String ANSI_RESET = "\u001B[0m";
    static final int M = (int) 1e9 + 7;
    static final long MM = (long) M * M;
    static final int MAX = Integer.MAX_VALUE;
    static final int MIN = Integer.MIN_VALUE;
    static final int SIZE = (int) 1e9 * 2;
    static ArrayList<Integer> primes = new ArrayList<>();
    //static Scanner sc = new Scanner(System.in);
    static FastReader sc = new FastReader();
    static long startTime;
    static long endTime;
    static boolean[] prime;
    static int[] visited;
    static ArrayList<ArrayList<Integer>> graph;
    static ArrayList<Integer> dfs;
    static boolean isCyclic = false;

    public static int swap(int... args) {
        return args[0];
    }

    public static void main(String[] args) throws IOException {
        do {
            startTime = currentTimeMillis();
            //setOut(new PrintStream("output"));
            //setIn(new FileInputStream("input"));
          int T = sc.nextInt();while (T-- != 0)
            {
                solve();

            }
            endTime = currentTimeMillis();
            long duration = endTime - startTime;
            //out.println(duration);
            if (false) {
                out.println(max(3, 2));
                Integer[] ARRAY = new Integer[2];
                ArrayList<Integer> LIST = new ArrayList<>();
                LIST.add(2);
                // sort(LIST, reverseOrder());
                LIST.sort(reverseOrder());
                sort(ARRAY, reverseOrder());
                out.println(LIST + " " + Arrays.toString(ARRAY));
            }
        } while (false);
    }

    public static void solve(){
/////////////////////////////////////////////////////////////////////
        int n =sc.nextInt();
        int [] arr= new int[n];
        for (int i = 0; i < n; i++) {
            arr[i]=sc.nextInt();
        }
        long temp =2L;
        for (int i = 0; i < n; i++) {
            if (arr[i] % temp == 0) {
                out.println("NO");
                return;
            }
                if (temp * (i + 3L) > 0) {
                    temp *= (i + 3L);
                }

        }
        out.println("YES");
///////////////////////////////////////////////////////////////////////

    }
    static void dfs(int src) {
        visited[src] = 1;
        for (Integer integer : graph.get(src)) {
            if (visited[integer] != 1) {
                dfs(integer);
            }
        }
        dfs.add(src);

    }

    static void detectCycle(int src) {
        visited[src] = 2;
        for (Integer integer : graph.get(src)) {
            if (visited[integer] == 0) {
                detectCycle(integer);
            } else if (visited[integer] == 2) {
                isCyclic = true;
                return;
            }

        }
        visited[src] = 1;
    }

    static <Array, Target> int count(Array[] array, Target target) {
        int cn = 0;
        for (Array value : array) {
            if (value.equals(target)) cn++;
        }
        return cn;
    }

    static int count(String string, char target) {
        int cn = 0;
        for (int i = 0; i < string.length(); i++) {
            if (string.charAt(i) == target) cn++;
        }
        return cn;
    }

    static <Array> void revArray(Array[] arr) {
        int n = arr.length;
        for (int i = 0; i < n / 2; i++) {
            Array temp = arr[i];
            arr[i] = arr[n - i - 1];
            arr[n - i - 1] = temp;
        }

    }

    static <Array> void printArray(Array[] arr) {
        int n = arr.length;
        for (Array array : arr) out.print(array + " ");
        out.println();
    }

    static void yes() {
        out.println("YES");
    }

    static void no() {
        out.println("NO");
    }

    public static boolean isPal(String s) {
        StringBuilder stringBuilder = new StringBuilder(s);
        return s.equals(stringBuilder.reverse().toString());
    }

    public static int lowerBound(Integer[] array, int length, int value) {
        int low = -1;
        int hi = length;
        while (low + 1 < hi) {
            int mid = (low + hi) / 2;
            if (array[mid] <= value) {
                low = mid;
            } else {
                hi = mid;
            }
        }
        return low;
    }

    public static int upperBound(Integer[] array, int length, int value) {
        int low = -1;
        int hi = length;
        while (low + 1 < hi) {
            int mid = (low + hi) >> 1;
            if (array[mid] >= value) {
                hi = mid;
            } else low = mid;
        }
        return hi;
    }

    public static int binarySearch(Integer[] arr, int length, int value) {
        int low = 0;
        int hi = length - 1;
        int ans = -1;
        while (low <= hi) {
            int mid = (low + hi) >> 1;
            if (arr[mid] > value) {
                hi = mid - 1;
            } else if (arr[mid] < value) {
                low = mid + 1;
            } else {
                ans = mid;
                break;
            }
        }
        return ans;
    }

    public static int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }

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

    public static int countDivs(int n) {
        int cn = 0;
        int sqr = (int) Math.sqrt(n);
        for (int i = 1; i <= sqr; ++i) {
            if (n % i == 0) {
                ++cn;
            }
        }
        cn *= 2;
        if (sqr * sqr == n) cn--;
        return cn;
    }

    static void prime(int x) {
        //sieve algorithm. nlog(log(n)).
        prime = new boolean[(x + 1)];
        Arrays.fill(prime, true);
        prime[0] = prime[1] = false;
        for (int i = 2; i * i <= x; i++)
            if (prime[i])
                for (int j = i * i; j <= x; j += i)
                    prime[j] = false;
    }

    static boolean isEven(long x) {
        return x % 2 == 0;
    }

    static boolean isPrime(long x) {
        boolean flag = true;
        int sqr = (int) Math.sqrt(x);
        if (x < 2) return false;
        for (int i = 2; i <= sqr; i++) {
            if (x % i == 0) {
                flag = false;
                break;
            }
        }
        return flag;
    }

    static long factorial(long x) {
        long total = 1;
        for (int i = 2; i <= x; i++)
            total = (total * i) % M;
        return total;
    }

    static long power(long x, long n) {
        if (n == 0) {
            return 1;
        }
        long pow = power(x, n / 2L);
        if ((n & 1) == 1) {
            return (x * (pow) * (pow));
        }
        return (pow * pow);
    }

    private static <T> String ts(T t) {
        if (t == null) {
            return "null";
        }
        try {
            return ts((Iterable) t);
        } catch (ClassCastException e) {
            if (t instanceof int[]) {
                String s = Arrays.toString((int[]) t);
                return "{" + s.substring(1, s.length() - 1) + "}";
            } else if (t instanceof long[]) {
                String s = Arrays.toString((long[]) t);
                return "{" + s.substring(1, s.length() - 1) + "}";
            } else if (t instanceof char[]) {
                String s = Arrays.toString((char[]) t);
                return "{" + s.substring(1, s.length() - 1) + "}";
            } else if (t instanceof double[]) {
                String s = Arrays.toString((double[]) t);
                return "{" + s.substring(1, s.length() - 1) + "}";
            } else if (t instanceof boolean[]) {
                String s = Arrays.toString((boolean[]) t);
                return "{" + s.substring(1, s.length() - 1) + "}";
            }
            try {
                return ts((Object[]) t);
            } catch (ClassCastException e1) {
                return t.toString();
            }
        }
    }

    private static <T> String ts(T[] arr) {
        StringBuilder ret = new StringBuilder();
        ret.append("{");
        boolean first = true;
        for (T t : arr) {
            if (!first) {
                ret.append(", ");
            }
            first = false;
            ret.append(ts(t));
        }
        ret.append("}");
        return ret.toString();
    }

    private static <T> String ts(Iterable<T> iter) {
        StringBuilder ret = new StringBuilder();
        ret.append("{");
        boolean first = true;
        for (T t : iter) {
            if (!first) {
                ret.append(", ");
            }
            first = false;
            ret.append(ts(t));
        }
        ret.append("}");
        return ret.toString();
    }

    public static void dbg(Object... o) {
        if (LOCAL) {
            System.err.print("Line #" + Thread.currentThread().getStackTrace()[2].getLineNumber() + ": [");
            for (int i = 0; i < o.length; i++) {
                if (i != 0) {
                    System.err.print(", ");
                }
                System.err.print(ts(o[i]));
            }
            System.err.println("]");
        }
    }

    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());
        }

        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;
        }
    }

    static class Pair implements Comparable<Pair> {
        private final int key;
        private final int value;

        public Pair(int key, int value) {
            this.key = key;
            this.value = value;
        }

        public int second() {
            return value;
        }

        @Override
        public int compareTo(Pair o) {
            return -Integer.compare(key, o.key);
        }

        @Override
        public String toString() {
            return "Pair{" + "x=" + key + ", y=" + value + '}';
        }
    }

}