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.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;

public class Solve {

	static long MOD = 998244353L;
	static long INF = 1000_000_000_000_000L + 100;
	static boolean isPrime[];

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner();
		PrintWriter pw = new PrintWriter(System.out);

		int t = sc.nextInt();
		while (t-- > 0) {
			int n = sc.nextInt();
			long a[] = sc.nextLongArray(n);

			long start = 2L;

			long mul = 1l;
			long pre = 1;
			boolean ok = true;
			for (int i = 0; i < n; i++) {

				pre = gcd(mul, start);

				mul = mul * (start) / pre;

				// 2 2*3
				if (a[i] % mul == 0) {
					ok = false;
					break;
				}
				start++;

			}

			pw.println(ok ? "YES" : "NO");

		}
		pw.flush();

	}

	static int LowerBound(int a[], int x, int start) { // x is the target value or key
		int ans = -1;

		int l = start, r = a.length;
		while (l + 1 < r) {
			System.out.println("lolk");

			int m = (l + r) >>> 1;
			if (a[m] >= x) {
				ans = m;
				r = m;
			} else
				l = m;
		}
		return ans;
	}

	static int UpperBound(int a[], int x, int start) {// x is the key or target value
		int ans = -1;

		int l = start, r = a.length;
		while (l + 1 < r) {
			int m = (l + r) >>> 1;
			if (a[m] <= x) {
				ans = m;
				l = m;
			} else
				r = m;
		}
		return ans;
	}

	static public boolean[] sieve(int n) {
		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) {
				// Update all multiples of p
				for (int i = p * p; i <= n; i += p)
					prime[i] = false;
			}
		}
		return prime;

	}

	public static ArrayList<Integer> primeFactors(int n) {
		ArrayList<Integer> set = new ArrayList<Integer>();

		// Print the number of 2s that divide n
		while (n % 2 == 0) {
			n /= 2;
			set.add(2);
		}

		// n must be odd at this point. So we can
		// skip one element (Note i = i +2)
		for (int i = 3; i * i <= n; i += 2) {
			// While i divides n, print i and divide n
			while (n % i == 0) {
				n /= i;
				set.add(i);
			}
		}

		if (n > 1)
			set.add(n);

		return set;

	}

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

		return gcd(b, a % b);

	}

	public static int[] swap(int data[], int left, int right) {

		// Swap the data
		int temp = data[left];
		data[left] = data[right];
		data[right] = temp;

		// Return the updated array
		return data;
	}

	public static long[] euclidExtended(long a, long b) {
		if (b == 0) {
			long ar[] = new long[] { 1, 0 };
			return ar;
		}
		long ar[] = euclidExtended(b, a % b);
		long temp = ar[0];
		ar[0] = ar[1];
		ar[1] = temp - (a / b) * ar[1];
		return ar;
	}

	public static long modInverse(long a, long m) {
		long ar[] = euclidExtended(a, m);
		return ((ar[0] % m) + m) % m;
	}

	// Fermat Theorem
	public static long ncr(int n, int r, long[] fact) {
		if (n == r)
			return 1;
		if (r == 1)
			return n;
		if (n == 0 || r == 0)
			return 1;
		return (fact[n] * modInverse(((long) fact[n - r]) * fact[r], MOD)) % MOD;
	}

	static void sort(int[] a) {
		ArrayList<Integer> l = new ArrayList<>();
		for (int i : a)
			l.add(i);
		Collections.sort(l);
		for (int i = 0; i < a.length; i++)
			a[i] = l.get(i);
	}

}

class Pair {
	int x, y;

	Pair(int x, int y) {
		this.x = x;
		this.y = y;
	}

}

class SegTree {
	int leftmost, rightmost, sum;
	SegTree lChild, rChild;

	public SegTree(int leftmost, int rightmost) {
		this.leftmost = leftmost;
		this.rightmost = rightmost;
	}

	public void update(int index, int val) {
		sum++;
		if (leftmost == rightmost) {
			return;
		}
		if (lChild == null)
			makeKids();
		if (index <= lChild.rightmost)
			lChild.update(index, val);
		else
			rChild.update(index, val);
	}

	public void makeKids() {
		int mid = (leftmost + rightmost) / 2;
		lChild = new SegTree(leftmost, mid);
		rChild = new SegTree(mid + 1, rightmost);
	}

	public int query(int l, int r) {
		if (l <= leftmost && r >= rightmost)
			return sum;
		if (l > rightmost || r < leftmost)
			return 0;
		if (lChild == null)
			return 0;
		return lChild.query(l, r) + rChild.query(l, r);
	}
}

class UnionFind {
	int[] p, rank, setSize;
	int numSets;

	public UnionFind(int N) {
		p = new int[numSets = N];
		rank = new int[N];
		setSize = new int[N];
		for (int i = 0; i < N; i++) {
			p[i] = i;
			setSize[i] = 1;
		}
	}

	public int findSet(int i) {
		return p[i] == i ? i : (p[i] = findSet(p[i]));
	}

	public boolean isSameSet(int i, int j) {
		return findSet(i) == findSet(j);
	}

	public void unionSet(int i, int j) {
		if (isSameSet(i, j))
			return;
		numSets--;
		int x = findSet(i), y = findSet(j);
		if (rank[x] > rank[y]) {
			p[y] = x;
			setSize[x] += setSize[y];
		} else {
			p[x] = y;
			setSize[y] += setSize[x];
			if (rank[x] == rank[y])
				rank[y]++;
		}
	}

	public int numDisjointSets() {
		return numSets;
	}

	public int sizeOfSet(int i) {
		return setSize[findSet(i)];
	}
}

class Scanner {
	BufferedReader br;
	StringTokenizer st;

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

	String next() throws IOException {
		while (st == null || !st.hasMoreElements())
			st = new StringTokenizer(br.readLine());
		return st.nextToken();
	}

	int nextInt() throws NumberFormatException, IOException {
		return Integer.parseInt(next());
	}

	int[] nextIntArray(int n) throws NumberFormatException, IOException {
		int a[] = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = Integer.parseInt(next());
		return a;
	}

	long nextLong() throws NumberFormatException, IOException {
		return Long.parseLong(next());
	}

	long[] nextLongArray(int n) throws NumberFormatException, IOException {
		long a[] = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = Long.parseLong(next());
		return a;
	}

	double nextDouble() throws NumberFormatException, IOException {
		return Double.parseDouble(next());
	}
}