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.util.*;
import java.io.*;
public class Test {
	public static void main(String[] args) throws IOException, InterruptedException {
	   Scanner sc = new Scanner(System.in);
	   PrintWriter pw = new PrintWriter(System.out);
	   int t = sc.nextInt();
	   while(t-->0) {
		   int n = sc.nextInt();
		   int [] arr = new int [n];
		   boolean can = true;
		   for(int i = 0;i<n;i++) {
			   arr[i] = sc.nextInt();
			   
		   } 
		   long mul = 1;
		   for  (long i = 1;i<=n;i++) {
			   if (mul< 1000000000) {
			   mul = mul * (i+1);}
			   if (arr[(int)(i-1)]% mul ==0) {
				   can = false;
			   }
		   }
		   System.out.println(can ?"YES":"NO");
	   }
	  }
	static Pair extendedEuclid (long a , long b) {
		if (b==0) {
			return new Pair (1,0);
		}
		Pair temp = extendedEuclid(b, a%b);
		return new Pair (temp.y,temp.x-(a/b)*temp.y);
	}
	static ArrayList<Integer> primes;
	static ArrayList <Pair> primeFactors;
	static void primeFactorization(long n) {
		for(int i : primes) {
			int c = 0;
			while(n%i ==0) {
				c++;
				n/=i;
			}
			if(c!=0) {
				primeFactors.add(new Pair(i, c));
			}
		}
		if(n!=1) {
			primeFactors.add(new Pair(n, 1));
		}
	}
	static  void sieveOfEratosthenes(int n)
	    {
	        // Create a boolean array "prime[0..n]" and initialize
	        // all entries it as true. A value in prime[i] will
	        // finally be false if i is Not a prime, else true.
	        boolean prime[] = new boolean[n+1];
	        for(int i=0;i<=n;i++)
	            prime[i] = true;
	         
	        for(int p = 2; p*p <=n; p++)
	        {
	            // If prime[p] is not changed, then it is a prime
	            if(prime[p] == true)
	            {
	            	primes.add(p);
	                // Update all multiples of p
	                for(int i = p*p; i <= n; i += p)
	                    prime[i] = false;
	            }
	        }}
	static void paint (int i,int j,int k) {
		painted[i][j] = true;
		for(int c = 1;c<=k;c++) {
			painted[i-c][j+c]=true;
			painted[i-c][j-c] = true;
		}
	}
	static long gcd1(long a, long b) {
		if(b==0) {
			return a;
		}
		return gcd1 (b, a%b);
	}
	static boolean canMoveDiagonalRight(int i, int j) {
		if (i-1>=0&&j+1<m&&map[i-1][j+1]=='*') {
			return true;
		}
		return false;
	}
	static int longestIncreasingSubsequence (int [] arr) {
		ArrayList<Integer> lcs = new ArrayList<Integer>();
		for(int i = 0;i<arr.length;i++) {
	         int ans = -1;
	         int l = 0;
	         int r = lcs.size()-1;
	         while(l<=r) {
	        	 int mid = (l+r)/2;
	        	 if(arr[lcs.get(mid)]>=arr[i]) {
	        		 ans = mid;
	        		 r = mid -1;
	        	 }
	        	 else {
	        		 l = mid +1;
	        	 }
	         }
	         if(ans ==-1) {
	        	 lcs.add(i);
	         }
	         else {
	        	 lcs.set(ans, i);
	         }
	         for(Integer e: lcs) {
	        	// System.out.print(e+" ");
	        	 
	         }
	        // System.out.println();
		}
		
		return lcs.size();
	}
	static boolean canMoveDiagonalLeft(int i, int j) {
		if (i-1>=0&&j-1>=0&&map[i-1][j-1]=='*') {
			return true;
		}
		return false;
	}
    static int countDiagonal(int start, int end) {
    	int countRight = 0;
    	int countLeft = 0;
    	int i = start;
    	int j = end ;
    	while(canMoveDiagonalRight(i, j)) {
    		countRight++;
    		i = i-1;
    		j = j+1;
    	}
    	i = start;
        j = end ;
    	while(canMoveDiagonalLeft(i, j)) {
    		countLeft++;
    		i = i-1;
    		j = j-1;
    	}
    	return Math.min(countLeft, countRight);
    }
    static boolean [][] painted;
	static char [][]map ;
	//static int k;
	static long cost (int k ) {
		Long [] costs = new Long[n];
		for(int i = 0;i<n;i++) {
			costs [i] = arr[i]*1l + (i+1)*k*1l;
			
		}
		long ans = 0;
		Arrays.sort(costs);
		for(int i  = 0;i<k;i++) {
			ans += costs[i];
		}
		return ans;
	}
	static long [] a;
	static long [] b;
	static int k;
	//static  HashMap< String, Boolean> map;
	static  long [] arr;
	static LinkedList<Integer> first;
	static LinkedList<Integer> second;
	
	static Pair [] islands;
    static HashSet<Integer> special ;
    
	

    	
    	
    
    static ArrayList <StringBuilder> ans ;
    
   
    static int mod=1000000007;  
    static int n;
    static int m;
    static int [][][]dp;
	static int bitCount (int msk) {
		int comp = 1;
		int count = 0;
		while(comp<=msk) {
			if((msk&comp)!=0) {
				count++;
			}
			comp = comp<<1;
		}
		return count;
	}

		   static class triple {
	            int u;
	            int v;
	            int z;
	 
	            public triple(int u, int v, int z) {
	                this.u = u;
	                this.v = v;
	                this.z = z;
	            }
	 
	            public String toString() {
	                return "triple{" +
	                        "u=" + u +
	                        ", v=" + v +
	                        ", z=" + z +
	                        '}';
	            }
	 
	            public boolean equals(Object o) {
	                if (this == o) return true;
	                if (o == null || getClass() != o.getClass()) return false;
	                triple triple = (triple) o;
	                return u == triple.u &&
	                        v == triple.v &&
	                        z == triple.z;
	            }
	 
	            public int hashCode() {
	                return Objects.hash(u, v, z);
	            }}
	 
 
			
 
 
 
	static class Pair  {
		public long x;
		public long y;
		public Pair (long x, long y) {
			this.x = x;
			this.y = y;
			
		}
		public double distance( Pair p) {
			return Math.sqrt((y-p.y)*(y-p.y)+(x-p.x)*(x-p.x));
		}
		@Override
		public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Pair triple = (Pair) o;
            return x == triple.x &&
                    y == triple.y ;
                
        }
		
		
	}static long modPow(long a, long x, long p) {
	    //calculates a^x mod p in logarithmic time.
	    long res = 1;
	    while(x > 0) {
	        if( x % 2 != 0) {
	            res = (res * a) % p;
	        }
	        a = (a * a) % p;
	        x /= 2;
	    }
	    return res;
	}
 
	static long modInverse(long a, long p) {
	    //calculates the modular multiplicative of a mod m.
	    //(assuming p is prime).
	    return modPow(a, p-2, p);
	}
	static long [] fact;
	static long nCr1(int n, int r,long mod)
	{ //System.out.println(r);
	   long numerator = fact[n]%mod;
	  // System.out.println(r+" "+(n-r));
	   long deno = ((fact[r]%mod)*(fact[n-r]%mod))%mod;
	
	    return (numerator*modInverse(deno,mod))%mod;
	}
 
	static ArrayList <Integer> prime;
	 static void simpleSieve(int limit)
	    {   
	        // Create a boolean array "mark[0..n-1]" and initialize
	        // all entries of it as true. A value in mark[p] will
	        // finally be false if 'p' is Not a prime, else true.
	        boolean mark[] = new boolean[limit+1];
	         
	        for (int i = 0; i < mark.length; i++)
	            mark[i] = true;
	      
	        for (int p=2; p*p<limit; p++)
	        {
	            // If p is not changed, then it is a prime
	            if (mark[p] == true)
	            {
	                // Update all multiples of p
	                for (int i=p*p; i<limit; i+=p)
	                    mark[i] = false;
	            }
	        }
	      
	        // Print all prime numbers and store them in prime
	        for (int p=2; p<limit; p++)
	        {
	            if (mark[p] == true)
	            {
	                prime.add(p);
	               // System.out.print(p + "  ");
	            }
	        }
	    }
 
	 
	 public static long gcd (long a, long b ) {
		 if(b==0) {
			 return a;
		 }
		 else {
			 return gcd1 (b, a%b);
		 }
	 }
	 
 static class Scanner {
 		StringTokenizer st;
 		BufferedReader br;
  
 		public Scanner(InputStream s) {
 			br = new BufferedReader(new InputStreamReader(s));
 		}
        public Scanner(FileReader r) {
        	br = new BufferedReader(r);
        }
 		public boolean hasNext() {
 			// TODO Auto-generated method stub
 			return false;
 		}
  
 		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 boolean ready() throws IOException {
 			return br.ready();
 		}
  
 	}
}