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 sys import stdin,stdout
for _ in range(int(stdin.readline())):
    n=int(stdin.readline())
    # a,b,c,n=list(map(int,stdin.readline().split()))
    f=2;A=B=C=-1;f1=[]
    while f*f<=n:
        if n%f==0:
            f1+=[f]
        f+=1
    nn=len(f1)
    for i in range(nn):
        for j in range(i+1,nn):
            c=n//(f1[i]*f1[j])
            if c*f1[i]*f1[j]==n and c!=f1[i] and c!=f1[j]:
                A,B,C=f1[i],f1[j],c
                break
    if A==-1:
        print('NO')
    else:
        print('YES')
        print(A,B,C)