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
def fact(n):
    ans = 1
    for i in range(2, n+1):
        ans*= i
    return ans
def comb(n, c):
    return fact(n)//(fact(n-c)*c)

for _ in range(int(input())):
    n= int(input())
    ans = []
    for i in range(2, int(math.sqrt(n))+1):
        if(n%i==0 and i not in ans):
            n//=i
            ans.append(i)
            break
    for i in range(2,int(math.sqrt(n))+1):
        if(n%i==0 and i not in ans):
            n//=i
            ans.append(i)
            break
    if(len(ans)<2 or n==1 or n in ans):
        print('NO')
    else:
        ans.append(n)
        print('YES')
        print(ans[0], ans[1], ans[2])