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.lang.reflect.Array;
import java.math.BigInteger;
import java.sql.SQLOutput;
import java.text.DateFormat;
import java.text.Format;
import java.text.ParseException;
import java.text.SimpleDateFormat;
import java.time.LocalDateTime;
import java.util.*;
import java.io.*;
import java.math.*;
import java.security.*;
import java.text.*;

import static java.util.Comparator.*;
import static java.util.stream.Collectors.*;

public class file {



    private static final Scanner sc = new Scanner(System.in);
    private static String s;
    private static int[] arr;
    private static HashSet<Long> set;
    private static HashMap<Character, Integer> cmap;
    private static Map<Long, Long> Lmap;
    private static Map<Integer, Integer> map;
    private static Stack<Integer> stk;
    private static ArrayList<Integer>[] graph;
    private static boolean[] visited;
    private static ArrayList<Integer> list;
    private static ArrayList<Long> Llist;

    private static final int MOD = 1000000007;

    //find max of array
    private static int findMax(int[] arr) {
        int max = Integer.MIN_VALUE;
        for (int x : arr) {
            max = Math.max(x, max);
        }
        return max;
    }

    // print an array
    private static void printArray(int[] arr) {
        for (int x : arr) {
            System.out.print(x + " ");
        }
        System.out.println();
    }

    //DFS
    private static int dfs(int curr, int prev) {
        int count = 1;
        for (int next : graph[curr]) {
            if (next==prev) continue;
            long new_count = dfs(next, curr);
            Llist.add(new_count* (graph.length - new_count));
            count += new_count;
        }
        return count;
    }

    private static int min_index(int first, int last) {
        int ind = 0, min = Integer.MAX_VALUE;
        for (int i = first; i <= last; i++) {
            if (arr[i] < min) {
                min = arr[i];
                ind = i;
            }
        }
        return ind;
    }

    private static long recurse(int first, int last) {
        int ind = min_index(first, last);
        int min = arr[ind];
        if (first > last) {
            return 0;
        } else {
            return Math.min(last-first + 1, recurse(first, ind - 1) + recurse(ind + 1, last) + min - Math.max(arr[first - 1], arr[last + 1]));
        }
    }

    private static long sum(long y) {
        long sum = 0;
        while (y > 0) {
            sum += (y%10);
            y /= 10;
        }
        return sum;
    }

    private static void popArray(int[] arr) {
        for (int i = 0; i < arr.length; i++) {
            arr[i] = sc.nextInt();
        }
    }

    private static int max(int a, int b, int c) {
        return Math.max(max(a,b),c);
    }

    private static int max(int a, int b) {
        return Math.max(a,b);
    }

    private static int min(int a, int b) {
        return Math.min(a,b);
    }

    private static int dfs(int a, ArrayList<Integer>[] G, boolean[] visited, int c, int dest) {
        int ans = 0;
        if (!visited[a]) {
            visited[a] = true;
            for (int k : G[a]) {
                if (k == dest) {
                    return c;
                }
                else if (!visited[k])
                    ans += dfs(k, G, visited, c + 1, dest);
            }
        }
        return ans;
    }

    private static int dbfs(int a, int[] time, ArrayList<Integer>[] Graph) {
        if (time[a] >= 0) return time[a];
        int ans = 1;
        for (int k : Graph[a]) {
            ans += dbfs(k, time, Graph);
        }
        time[a] = ans;
        return ans;
    }



    public static List<List<Integer>> permuteUnique(int[] nums) {
        List<List<Integer>> result = new LinkedList<>();
        Arrays.sort(nums);
        boolean []used = new boolean[nums.length];
        dfs(result,nums, new ArrayList<>(),used);
        return result;

    }
    public static void dfs(List<List<Integer>> result , int []nums, List<Integer> current, boolean []used){
        if(current.size() == nums.length){

            result.add(new ArrayList(current));
            return;
        }

        for(int i = 0; i<nums.length;i++){
            if(used[i] == true) continue;
            if(i>0 && nums[i] == nums[i-1] && !used[i-1]) continue;
            current.add( nums[i]);
            used[i] = true;
            dfs(result , nums, current, used);
            current.remove(current.size()-1);
            used[i]  = false;
        }

    }

    public static int findMin(int[] arr) {
        int x = 0, t = arr[0];
        for (int i = 1; i < arr.length; i++) {
            if (arr[i]  < t) {
                x = i;
                t = arr[i];
            }
        }
        return x;
    }

    public static int[][] restoreMatrix(int[] rowSum, int[] colSum) {
        int[][] mat = new int[rowSum.length][colSum.length];
        while (true) {
            int a = findMin(rowSum);
            int b = findMin(colSum);
            if (rowSum[a] == Integer.MAX_VALUE || colSum[b] == Integer.MAX_VALUE) break;
            mat[a][b] = min(rowSum[a], colSum[b]);
            rowSum[a] -= mat[a][b];
            colSum[b] -= mat[a][b];
            if (rowSum[a] == 0) rowSum[a] = Integer.MAX_VALUE;
            if (colSum[b] == 0) colSum[b] = Integer.MAX_VALUE;
        }
        return mat;
    }


    private static int[] ans;

    private static boolean isPrime(int n)
    {
        if (n <= 1)
            return false;
        if (n <= 3)
            return true;
        if (n % 2 == 0 || n % 3 == 0)
            return false;
        for (int i = 5; i * i <= n; i = i + 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;
        return true;
    }

    private static void dfs2(int curr, int val) {
        ans[curr] = val;
        int newVal = val;
        if (newVal > 1) newVal = 1;
        else newVal = 2;
        for (int next : graph[curr]) {
            if (ans[next] > 0) continue;
            dfs2(next, newVal);
        }
    }

    static long gcd(long a, long b)
    {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }

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

    private static void foo(int testCase) {
        //take length of array as input
        int n = sc.nextInt();
        int[] arr = new int[n];
        ArrayList<Integer> inc = new ArrayList<>();
        for (int i = 0; i < n; i++)
            arr[i] = sc.nextInt();
        long lcm = 2;
        if (arr[0] % 2 == 0) {
            System.out.println("NO");
            return;
        }
        for (int i = 1; i < n; i++) {
            if (lcm <= 1000000000) {
                lcm = lcm(lcm, i + 2);
                if (arr[i] % lcm == 0) {
                    System.out.println("NO");
                    return;
                }
            } else break;
        }
        System.out.println("YES");
    }



    public static void main(String[] args) throws IOException {
        int t = sc.nextInt();
        for (int i = 0; i < t; i++) {
            foo(i + 1);
        }
    }


}