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:
# -*- coding: utf-8 -*-
"""
Created on Sun Feb  2 11:27:04 2020

@author: pc
"""
'''
times = int(input())
for _ in range(times):
    testified_number = int(input())
    able = 0
    for factor in range(2,testified_number):
        if testified_number % factor == 0:
            testified_number_new = testified_number // factor
            for factor_new in range(factor + 1,testified_number_new):
                if testified_number_new % factor_new == 0 and testified_number_new // factor_new > factor_new:
                    able = 1
                    b = factor_new
                    c = testified_number_new // factor_new
                    break
            if able == 1:
                a = factor
                break
    if able:
        print("YES")
        print(a,b,c)
    else:
        print('NO')
'''

'''
times = int(input())
testified_numbers = [0] * times
for i in range(times):
    testified_numbers[i] = int(input())
M = max(testified_numbers)

judge = [False] * 2 + [True] * (M-1)
for i in range(M+1):
    if judge[i]:
        for j in range(2*i,M+1,i):
            judge[j]=False

for i in range(times):
    able = 0
    number = testified_numbers[i]
    factors = {}
    if not judge[number]:
        for factor in range(2,int(M**(1/3))+1):
            if judge[factor] and number % factor == 0:
                while number % factor == 0:
                    number = number // factor
                    if factor in factors:
                        factors[factor] += 1
                    else:
                        factors[factor] = 1
                if len(factors) == 3:
                        able = 1
                        a = list(factors.keys())[0]
                        b = list(factors.keys())[1]
                        c = testified_numbers[i] // (a*b)
                        break
                elif len(factors) == 2 and list(factors.values()) != [1,1] and list(factors.values()) != [1,2] and list(factors.values()) != [2,1]:
                    able = 1
                    a = list(factors.keys())[0]
                    b = list(factors.keys())[1]
                    c = testified_numbers[i] // (a*b)
                    break 
                elif len(factors) == 1 and list(factors.values())[0] >= 6:
                    able = 1
                    a = list(factors.keys())[0]
                    b = list(factors.keys())[0]**2
                    c = testified_numbers[i] // (a*b)
                    break
                    
    if able:
        print("YES")
        print(a,b,c)
    else:
        print('NO')
'''        

for _ in range(int(input())):
    n = int(input())
    a = []
    for i in range(2, int(n**0.5)+1):
        if n % i == 0:
            a.append(i)
            n = n//i
            if len(a) == 2:
                break
    if len(a) == 2 and n > a[1]:
        print('YES')
        print(a[0],a[1],n)
    else:
        print('NO')