Problem: 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 

Solution (in PYTHON3):

Solution:
import math
def printDivisors(n) : 
    i = 2
    factors = {}
    while i <= math.sqrt(n): 
        if (n % i == 0) : 
            if (n // i == i) : 
                factors[i] = 1
            else : 
                factors[n//i] = 1
                factors[i] = 1
        i = i + 1
    return factors

for t in range(int(input())):
    n = int(input())
    f = printDivisors(n)
    factors = list(f.keys())
    factors.sort()
    if len(factors) < 3:
        print('NO')
    else:
        i = 1
        flag = False
        while i < len(factors)//2:
            temp = factors[0]*factors[i]
            try:
                x = f[temp]
                if n//temp != factors[0] and n//temp != factors[i]:
                    print('YES')
                    print(factors[0],factors[i],n//temp)
                    flag = True
                    break
                else:
                    i += 1
            except KeyError:
                i += 1
        if not(flag):
            print('NO')