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:
'''
5
64
32
97
2
12345
'''


def mi():
    return map(int, input().split())

for _ in range(int(input())):
    n = int(input())
    i = 2
    found=0
    while i*i<=n:
        if (n % i == 0): 
            n1 = n//i
            j=2
            comp=0
            while j*j<=n1:
                if n1%j==0:
                    comp=1
                    if i==n1//j or i==j or (n1//j==j) or n//j==1 or j==1:
                        j+=1
                        continue
                    else:
                        if found or n1//j==1 or j==1:
                            break
                        found = 1
                        print('YES')
                        print(i,n1//j,j)
                j+=1
        i+=1
    
    if not found:
        print ('NO')