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 ceil,sqrt
def kFactors(n, k=3): 
    a = []
    for i in range(2, ceil(sqrt(n))): 
        if(n%i==0):
            n = n / i
            a.append(i) 
    if n > 2: 
        a.append(n)
    a = list(set(a))
    if len(a) < k: 
        return [-1]
    return [a[0],a[1]]

for i in range(int(input())):
    n = int(input())
    a = kFactors(n)
    if(a[0]==-1):
        print('NO')
    else:
        print('YES')
        print(int(a[0]),int(a[1]),int(n//(a[0]*a[1])))
