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 sys
import time
import os
from io import BytesIO, IOBase

M=10**9+7
BUFSIZE = 8192
class FastIO(IOBase):
    newlines = 0
 
    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None
 
    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()
 
    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()
 
    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)
 
 
class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")
 
 
def print(*args, **kwargs):
    """Prints the values to a stream, or to sys.stdout by default."""
    sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout)
    at_start = True
    for x in args:
        if not at_start:
            file.write(sep)
        file.write(str(x))
        at_start = False
    file.write(kwargs.pop("end", "\n"))
    if kwargs.pop("flush", False):
        file.flush()
 
 
if sys.version_info[0] < 3:
    sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
else:
    sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
 
def inputf(): 
    return sys.stdin.readline().rstrip("\r\n")  
 
 
def printf(var): 
    sys.stdout.write(str(var)+"\n")  
 
 
def get_ints(): 
    return list(map(int, inputf().split()))
 
 
def get_string(): 
    return list(map(str, inputf().split()))





global maximum
 
 
def _lis(arr, n):
 
    global maximum
 
    if n == 1:
        return 1
 
    maxEndingHere = 1
    for i in range(1, n):
        res = _lis(arr, i)
        if arr[i-1] < arr[n-1] and res+1 > maxEndingHere:
            maxEndingHere = res + 1
 
    maximum = max(maximum, maxEndingHere)
 
    return maxEndingHere
 
 
def LIS(arr):
 
    global maximum
 
    n = len(arr)
 
    maximum = 1
 
    _lis(arr, n)
 
    return maximum
 

def binary_search(data, elem):
    
    low = 0
    high = len(data) - 1
    while low <= high:
      
        middle = (low + high)//2
        if data[middle] == elem:
            return middle
            
        elif data[middle] > elem:

            high = middle - 1
        else:
            low = middle + 1

    return middle   

def upper_bound(my_list, key):
    large = len(my_list) -1
    small = 0

    while (small <= large):
        mid = (small + large) // 2
        if my_list[mid] < key:
            small = mid + 1
        elif my_list[mid] > key:
            large = mid - 1
        else:
            return mid
    if my_list[mid]>key:
        return mid
    else:
        return mid+1


def lower_bound(my_list, key):
    large = len(my_list) -1
    small = 0

    while (small <= large):
        mid = (small + large) // 2
        if my_list[mid] < key:
            small = mid + 1
        elif my_list[mid] > key:
            large = mid - 1
        else:
            return mid
    if my_list[mid]<key:
        return mid
    else:
        return mid-1


a=[]
def SieveOfEratosthenes(n):
    
	prime = [True for i in range(n+1)]
	p = 2
	while (p * p <= n):

		if (prime[p] == True):

			for i in range(p * p, n+1, p):
				prime[i] = False
		p += 1

	for p in range(2, n+1):
		if prime[p]:
			a.append(p)

def roman_number(x):
    if x > 15999:
        return
    value = [5000, 4000, 1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1]
    symbol = ["F", "MF", "M", "CM", "D", "CD", "C", "XC", "L", "XL", "X", "IX", "V", "IV", "I"]
    roman = ""
    i = 0
    while x > 0:
        div = x // value[i]
        x = x % value[i]
        while div:
            roman += symbol[i]
            div -= 1
        i += 1
    return roman

def maxSubArraySum(a,size):
     
    max_so_far = a[0]   
    max_ending_here = 0
     
    for i in range(0, size):
        max_ending_here = max_ending_here + a[i]
        if max_ending_here < 0:
            max_ending_here = 0
         
        elif (max_so_far < max_ending_here):   
            max_so_far = max_ending_here
             
    return max_so_far

    
def prefixSum(test_list):
    res = [sum(test_list[ : i + 1]) for i in range(len(test_list))]
    return res

"""
def find_shortest_path(graph, start, end, path):
    path = path + [start]
    if start == end:
        return path
    if start not in graph:
        return None
    shortest = None
    for node in graph[start]:
        if node not in path:
            newpath = find_shortest_path(graph, node, end, path)
            if newpath:
                if not shortest or len(newpath) < len(shortest):
                    shortest = newpath
    return shortest
""" 

"""
def dfs(root,nodeVal,nodeConnection,visited):
    leftVal = nodeVal[root][0]
    rightVal = nodeVal[root][1]
    solution = []
    if nodeConnection[root]:
        visited.add(root)
        for i in nodeConnection[root]:
            if i not in visited:
                solution.append(dfs(i,nodeVal,nodeConnection,visited))
        leftMax = 0
        rightMax = 0
        for i in solution:
            l, r = i
            leftMax += max(abs(leftVal - l[0]) + l[1], abs(leftVal - r[0]) + r[1])
            rightMax += max(abs(rightVal - l[0]) + l[1], abs(rightVal - r[0]) + r[1])
        return ((leftVal, leftMax), (rightVal, rightMax))
    else:
        return ((leftVal, 0), (rightVal, 0))
 
"""
 
"""
def BFS(adj,src,dist,paths,n):
    visited=[False]*n
    dist[src]=0
    paths[0]=1
    q=[src]
    visited[src]=True
    while(q):
        p=q.pop(0)
        for j in adj[p]:
            if not visited[j]:
                q.append(j)
                visited[j]=True
            if dist[j]>dist[p]+1:
                dist[j] = dist[p]+1
                paths[j] = paths[p]
            elif dist[j]==dist[p]+1:
                paths[j] +=paths[p]
    return paths
 
"""

testcase=int(inputf())
for test in range(0,testcase):
    n=int(inputf())
    a=get_ints()
    for i in range(0,n):
        if a[i]%(i+2)==0:
            print("NO")
            break
    else:
        print("YES")