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:
from math import sqrt
t = int(input())

for _ in range(t):
    n = int(input())
    ans = []
    for i in range(2, int(sqrt(n))+1):
        if len(ans) == 2 and n>ans[-1]:
            ans.append(n)
            n = 1
            break
        elif n%i==0:
            ans.append(i)
            n//=i
        if n==1:
            break
        if len(ans) and n<=ans[-1]:
            break
        
    if n!=1 or len(ans)<3:
        print("NO")
    else:
        print("YES")
        prod = 1
        for i in range(2, len(ans)):
            prod*=ans[i]
        print(ans[0], ans[1], prod)