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.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.util.Arrays;
import java.util.Random;
import java.io.FileWriter;
import java.io.PrintWriter;
/*
    Solution Created: 18:01:44 30/10/2021
    Custom Competitive programming helper.
*/
public class Main {
	
	public static void solve() {
		int n = in.nextInt();
		int[] a = in.na(n);
		boolean ans = true;
		for(int i = 0; i<n&&ans; i++) {
			int mxDiv = i+2;
			ans &= prCheck(a[i], mxDiv);
		}
		out.yesNo(ans);
	}
	public static boolean prCheck(int n, int mxDiv) {
		for(int i = 2; i<=mxDiv; i++) if(n%i!=0) return true;
		return false;
    }
	public static void main(String[] args) {
		in = new Reader();
		out = new Writer();
		int t = in.nextInt();
		while(t-->0) solve();
		out.exit();
	}
	static Reader in; static Writer out;

static class Reader {
	static BufferedReader br;
	static StringTokenizer st;
	
	public Reader() {
		this.br = new BufferedReader(new InputStreamReader(System.in));
	}
	
	public Reader(String f){
		try {
			this.br = new BufferedReader(new FileReader(f));
		} catch (IOException e) {
			e.printStackTrace();
		}
	}
	
	public int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++) a[i] = nextInt();
		return a;
	}

	public double[] nd(int n) {
		double[] a = new double[n];
		for (int i = 0; i < n; i++) a[i] = nextDouble();
		return a;
	}
	
	public long[] nl(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++) a[i] = nextLong();
		return a;
	}

	public char[] nca() {
		return next().toCharArray();
	}

	public String[] ns(int n) {
		String[] a = new String[n];
		for (int i = 0; i < n; i++) a[i] = next();
		return a;
	}

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

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

	public Long nextLong() {
		ensureNext();
		return Long.parseLong(st.nextToken());
	}

	public String next() {
		ensureNext();
		return st.nextToken();
	}
	
	public String nextLine() {
		try {
			return br.readLine();
		} catch (Exception e) {
			e.printStackTrace();
			return null;
		}
	}
	
	private void ensureNext() {
		if (st == null || !st.hasMoreTokens()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (IOException e) {
				e.printStackTrace();
			}
		}
	}
}

static class Util{
		private static Random random = new Random();
		static long[] fact;
		
		public static void initFactorial(int n, long mod) {
			fact = new long[n+1];
			fact[0] = 1;
			for (int i = 1; i < n+1; i++) fact[i] = (fact[i - 1] * i) % mod;
		}
		
		public static long modInverse(long a, long MOD) {
			long[] gcdE = gcdExtended(a, MOD);
			if (gcdE[0] != 1) return -1; // Inverted doesn't exist
			long x = gcdE[1];
			return (x % MOD + MOD) % MOD;
		}
		
		public static long[] gcdExtended(long p, long q) {
			if (q == 0) return new long[] { p, 1, 0 };
			long[] vals = gcdExtended(q, p % q);
			long tmp = vals[2];
			vals[2] = vals[1] - (p / q) * vals[2];
			vals[1] = tmp;
			return vals;
		}
		
		public static long nCr(int n, int r, long MOD) {
			if (r == 0) return 1;
			return (fact[n] * modInverse(fact[r], MOD) % MOD * modInverse(fact[n - r], MOD) % MOD) % MOD;
		}
		
		public static long nCr(int n, int r) {
			return (fact[n]/fact[r])/fact[n-r];
		}
		
		public static long nPr(int n, int r, long MOD) {
			if (r == 0) return 1;
			return (fact[n] * modInverse(fact[n - r], MOD) % MOD) % MOD;
		}
		public static long nPr(int n, int r) {
			return fact[n]/fact[n-r];
		}
		
		public 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; 
	    }
		
	    public static boolean[] getSieve(int n) {
	        boolean[] isPrime = new boolean[n+1];
	        for (int i = 2; i <= n; i++) isPrime[i] = true;
	        for (int i = 2; i*i <= n; i++) if (isPrime[i]) 
	                for (int j = i; i*j <= n; j++) isPrime[i*j] = false;
	        return isPrime;
	    }
	    
	    static long pow(long x, long pow, long mod){
	    	long res = 1;
	    	x = x % mod;
	    	if (x == 0) return 0;
	    	while (pow > 0){
	    		if ((pow & 1) != 0) res = (res * x) % mod;
	        	pow >>= 1;
	        	x = (x * x) % mod;
	    	}
	    	return res;
	    }
	    
	    public static int gcd(int a, int b) { 
	    	int tmp = 0;
	    	while(b != 0) {
	    		tmp = b;
	    		b = a%b;
	    		a = tmp;
	    	}
	    	return a;
	    }
	    
	    public static long gcd(long a, long b) { 
	    	long tmp = 0;
	    	while(b != 0) {
	    		tmp = b;
	    		b = a%b;
	    		a = tmp;
	    	}
	    	return a;
	    }
	    
	    public static int random(int min, int max) {
	    	return random.nextInt(max-min+1)+min;
	    }
	    
		public static void dbg(Object... o) { 
			System.out.println(Arrays.deepToString(o)); 
		}
		
		public static void reverse(int[] s, int l , int r) {
			for(int i = l; i<=(l+r)/2; i++) {
				int tmp = s[i];
				s[i] = s[r+l-i];
				s[r+l-i] = tmp;
			}
	    }
		
		public static void reverse(int[] s) {
			reverse(s, 0, s.length-1);
	    }
		
		public static void reverse(long[] s, int l , int r) {
			for(int i = l; i<=(l+r)/2; i++) {
				long tmp = s[i];
				s[i] = s[r+l-i];
				s[r+l-i] = tmp;
			}
	    }
		
		public static void reverse(long[] s) {
			reverse(s, 0, s.length-1);
	    }
		
		public static void reverse(float[] s, int l , int r) {
			for(int i = l; i<=(l+r)/2; i++) {
				float tmp = s[i];
				s[i] = s[r+l-i];
				s[r+l-i] = tmp;
			}
	    }
		
		public static void reverse(float[] s) {
			reverse(s, 0, s.length-1);
	    }
		
		public static void reverse(double[] s, int l , int r) {
			for(int i = l; i<=(l+r)/2; i++) {
				double tmp = s[i];
				s[i] = s[r+l-i];
				s[r+l-i] = tmp;
			}
	    }
		
		public static void reverse(double[] s) {
			reverse(s, 0, s.length-1);
	    }
		
		public static void reverse(char[] s, int l , int r) {
			for(int i = l; i<=(l+r)/2; i++) {
				char tmp = s[i];
				s[i] = s[r+l-i];
				s[r+l-i] = tmp;
			}
	    }
		
		public static void reverse(char[] s) {
			reverse(s, 0, s.length-1);
	    }
		
		public static <T> void reverse(T[] s, int l , int r) {
			for(int i = l; i<=(l+r)/2; i++) {
				T tmp = s[i];
				s[i] = s[r+l-i];
				s[r+l-i] = tmp;
			}
	    }
		
		public static <T> void reverse(T[] s) {
			reverse(s, 0, s.length-1);
	    }
		
		public static void shuffle(int[] s) {
	        for (int i = 0; i < s.length; ++i) {
	            int j = random.nextInt(i + 1);
	            int t = s[i];
	            s[i] = s[j];
	            s[j] = t;
	        }
	    }
		
	    public static void shuffle(long[] s) {
	        for (int i = 0; i < s.length; ++i) {
	            int j = random.nextInt(i + 1);
	            long t = s[i];
	            s[i] = s[j];
	            s[j] = t;
	        }
	    }
	    
	    public static void shuffle(float[] s) {
	        for (int i = 0; i < s.length; ++i) {
	            int j = random.nextInt(i + 1);
	            float t = s[i];
	            s[i] = s[j];
	            s[j] = t;
	        }
	    }
	    
	    public static void shuffle(double[] s) {
	        for (int i = 0; i < s.length; ++i) {
	            int j = random.nextInt(i + 1);
	            double t = s[i];
	            s[i] = s[j];
	            s[j] = t;
	        }
	    }
	    
	    public static void shuffle(char[] s) {
	        for (int i = 0; i < s.length; ++i) {
	            int j = random.nextInt(i + 1);
	            char t = s[i];
	            s[i] = s[j];
	            s[j] = t;
	        }
	    }
	    
	    public static <T> void shuffle(T[] s) {
	        for (int i = 0; i < s.length; ++i) {
	            int j = random.nextInt(i + 1);
	            T t = s[i];
	            s[i] = s[j];
	            s[j] = t;
	        }
	    }
	    
		public static void sortArray(int[] a) {
	        shuffle(a);
	        Arrays.sort(a);
	    }
		
		public static void sortArray(long[] a) {
			shuffle(a);
	        Arrays.sort(a);
	    }
		
		public static void sortArray(float[] a) {
			shuffle(a);
	        Arrays.sort(a);
	    }
		
		public static void sortArray(double[] a) {
			shuffle(a);
	        Arrays.sort(a);
	    }
		
		public static void sortArray(char[] a) {
			shuffle(a);
	        Arrays.sort(a);
	    }
		
		public static <T extends Comparable<T>> void sortArray(T[] a) {
	        Arrays.sort(a);
	    }
	}

static class Writer {
	private PrintWriter pw;
	public Writer(){
		pw = new PrintWriter(System.out);
	}
	
	public Writer(String f){
		try {
			pw = new PrintWriter(new FileWriter(f));
		} catch (IOException e) {
			e.printStackTrace();
		}
	}
	
	public void yesNo(boolean condition) {
		println(condition?"YES":"NO");
	}
	
	public void printArray(int[] a) {
		for(int i = 0; i<a.length; i++) print(a[i]+" ");
	}
	
	public void printlnArray(int[] a) {
		for(int i = 0; i<a.length; i++) print(a[i]+" ");
		pw.println();
	}
	
	public void printArray(long[] a) {
		for(int i = 0; i<a.length; i++) print(a[i]+" ");
	}
	
	public void printlnArray(long[] a) {
		for(int i = 0; i<a.length; i++) print(a[i]+" ");
		pw.println();
	}
	
	public void print(Object o) {
		pw.print(o.toString());
	}
	
	public void println(Object o) {
		pw.println(o.toString());
	}
	
	public void println() {
		pw.println();
	}
	
	public void flush() {
		pw.flush();
	}
	public void exit() {
		pw.close();
	}
}
}
