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 factorial
from collections import Counter
from sys import stdin
def RL(): return map(int, stdin.readline().rstrip().split() )
def comb(n, m): return factorial(n)/(factorial(m)*factorial(n-m)) if n>=m else 0
def perm(n, m): return factorial(n)//(factorial(n-m)) if n>=m else 0
def mdis(x1, y1, x2, y2): return abs(x1-x2) + abs(y1-y2)
mod = 1000000007
from math import gcd
# ------------------------------
from math import sqrt
N = int(input())
for _ in range(N):
    n = int(input())
    tag = False
    for i in range(2, int(sqrt(n))+1):
        if n%i==0:
            for j in range(2, int(sqrt(n//i))+1):
                if i!=j and (n//i)%j==0 and n//i//j!=j and n//i//j!=i and n//i//j!=1:
                    print("YES")
                    print(i, j, n//i//j)
                    tag = True

                if tag: break
            if tag: break
    else:
        print("NO")