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 
import math
for _ in range(int(input())):
    n=int(input())
    g=0
    for i in range(2,math.floor(math.sqrt(n))+1):
        if n%i==0:
            if n//i!=i:
                p=n//i
                for j in range(2,math.floor(math.sqrt(i))+1):
                    if i%j==0:
                        if i//j!=j and j!=p and p!=i//j:
                            g=1
                            l=[n//i,j,i//j]
                            break
                for j in range(2,math.floor(math.sqrt(p))+1):
                    if p%j==0:
                        if p//j!=j and i!=j and i!=p//j:
                            g=1
                            l=[j,p//j,i]
                            break
    if g==0:
        print("NO")
    else:
        print("YES")
        print(*l)