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