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
def func(N,x):
    val = N**0.5
    val = int(val)+1
    tem = 0
    for i in range(x+1,val):
        if(N%i==0):
            if(N//i>1 and N//i!=i):
                print("YES")
                print(x,i,N//i)
                tem = 1
                break
    if(tem==0):
        print("NO")
            

for _ in range(int(input())):
    N = int(input())
    val = N**0.5
    val = int(val)+1
    temp=0
    for i in range(2,val):
        if(N%i==0):
            if(N//i!=i):
                temp=1
                func(N//i,i)
                break
    if(temp==0):
        print("NO")