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:
import math
t=int(input())

for _ in range(t):
    n=int(input())
    raj=set()
    for i in range(2, math.ceil(math.sqrt(n))):
        if(n%i==0):
            raj.add(i)
            raj.add(n//i)
    flg=0
    for i in raj:
        a=i
        dup=n//a
        andro=set()
        for j in range(2, math.ceil(math.sqrt(dup))):
            if(dup%j==0):
                b=j
                c=dup//b
                if(b!=a and b!=c and c>1 and a!=c):
                    ans=[a,b,c]
                    ans=sorted(ans)
                    print("YES")
                    print(*ans)
                    flg=1
                    break
        if(flg==1):
            break
    if(not flg):
        print("NO")