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:
def main():
    def divisors(n):
        div = []
        for i in range(2, int(n**0.5)): #n//2 + 1):#int(n ** 0.5)):
            if n % i == 0:
                div.append(i)
                n //= i
            if len(div) == 2:
                if n not in div and n != 1:
                    div.append(n)
                break
            
        return div

        
        
    for _ in range(int(input())):
        n = int(input())
        
        d = divisors(n)
        #print(d)
        if len(d) < 3:
            print('NO')
            continue
        
        print('YES')
        print(*d)
        '''
        a = d[0]
        n = n // a
        b = d[1]
        c = n // b
        
        if c != 1 and c != b and c != a:
            print('YES')
            print(a, b, c)
        else:
            print('NO')'''
    
    

main()


'''
        i = 2
        while i < n and len(div) < 2:
            if n % i == 0:
                div.append(i)
                #t = n // i
                n //= i
            i += 1
        if n not in div:
            div.append(n)
        return div'''