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 
from math import sqrt
for i in range(int(input())):
    a=int(input())
    for j in range (2,int(sqrt(a))+1):
        if a%j==0:
            a=a//j
            for k in range(j+1,int(sqrt(a))+1):
                if a%k==0:
                    a=a//k
                    if a>k:
                        print("YES")
                        print(j,k,a)
                        break
                    else:
                        print("NO")
                        break
            else:
                print("NO")
                break
            break
    else:
        print("NO")