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 collections import defaultdict as dd
from sys import stdin
input=stdin.readline
for _ in range(int(input())):
    n=int(input())
    br=0
    for i in range(2,int(n**.5)+1):
        fl=0
        if n%i==0:
            fl=1
            x=i
            for j in range(2,int(i**.5)+1):
                if i%j==0 and len(set([j,i//j,n//i]))==3:
                    br=1
                    print('YES')
                    print(j,i//j,n//i)
                    break
            if br:
                break
            for j in range(2,int((n//i)**.5)+1):
                if (n//i)%j==0 and len(set([i,(n//i)//j,j]))==3:
                    br=1
                    print('YES')
                    print(i,(n//i)//j,j)
                    break
            if br:
                break
    if br:
        continue
    else:
        print('NO')