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:
# Why do we fall ? So we can learn to pick ourselves up.
from functools import reduce
def factors(n):
    k = sorted(list(set(reduce(list.__add__,
                     ([i,n//i] for i in range(1,int(n**0.5+1)) if n%i == 0)))))
    return k[1:]
def solve():
    n = int(input())
    f = factors(n)
    if len(f) < 3:
        print('NO')
    else:
        sss = 'NO'
        a, b, c = -1, -1, -1
        for i in range(0, len(f)):
            for j in range(i + 1, len(f)):
                temp = n // f[i]
                temp //= f[j]
                if temp in f and temp != f[i] and temp != f[j]:
                    a, b, c = f[i], f[j], temp
                    sss = 'YES'
                    break
            if sss == 'YES':
                break
        if sss == 'YES':
            print(sss)
            print(a, b, c)
        else:
            print(sss)
t = int(input())
for _ in range(0,t):
    solve()