Problem: You are given one integer number n. Find three distinct integers a, b, c such that 2 ≤ a, b, c and a ⋅ b ⋅ c = n or say that it is impossible to do it.

If there are several answers, you can print any.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases.

The next n lines describe test cases. The i-th test case is given on a new line as one integer n (2 ≤ n ≤ 10^9).

Output

For each test case, print the answer on it. Print "NO" if it is impossible to represent n as a ⋅ b ⋅ c for some distinct integers a, b, c such that 2 ≤ a, b, c.

Otherwise, print "YES" and any possible such representation.

Example

Input


5
64
32
97
2
12345


Output


YES
2 4 8 
NO
NO
NO
YES
3 5 823 

Solution (in PYTHON3):

Solution:
t = int(input())

def factorization(n):
    ind = []
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            ind.append(cnt)
            arr.append(i)

    if temp!=1:
        ind.append(1)
        arr.append(temp)

    if arr==[]:
        ind.append(1)
        arr.append(n)

    return arr, ind

for i in range(t):
    n = int(input())
    arr, ind = factorization(n)
    if len(arr) == 1:
        if ind[0] >= 6:
            print('YES')
            print(arr[0], arr[0]**2, arr[0]**(ind[0]-3))
        else:
            print('NO')
    elif len(arr) == 2:
        if ind[0] >= 3:
            print('YES')
            print(arr[0], arr[0]**2, (arr[0]**(ind[0]-3))*(arr[1]**ind[1]))
        elif ind[1] >= 3:
            print('YES')
            print(arr[1], arr[1]**2, (arr[1]**(ind[1]-3))*(arr[0]**ind[0]))
        elif ind[0] >= 2 and ind[1] >= 2:
            print('YES')
            print(arr[0], arr[1], (arr[0]**(ind[0]-1))*(arr[1]**(ind[1]-1)))
        else:
            print('NO')
    else:
        print('YES')
        print(arr[0], arr[1], (n//arr[0])//arr[1])