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
t = int(input())
for _ in range(t):
    n = int(input())
    nn = n
    fact = dict()
    i = 2
    while i <= math.sqrt(nn):
        if n % i == 0:
            n //= i
            try:
                fact[i] += 1
            except:
                fact[i] = 1
        else:
            i += 1
    if n != 1:
        fact[n] = 1
    if len(fact) == 0:
        print("NO")
        continue
    if len(fact) > 3:
        k = list(fact.keys())
        print("YES")
        print(k[0]**fact[k[0]], k[1]**fact[k[1]], end=" ")
        num = 1
        for i in range(2, len(k)):
            num *= k[i] ** fact[k[i]]
        print(num)
    if len(fact) == 3:
        print("YES")
        a, b, c = list(fact.keys())
        print(a**fact[a], b**fact[b], c**fact[c])
    if len(fact) == 1:
        k = list(fact.keys())[0]
        if fact[k] < 6:
            print("NO")
        else:
            print("YES")
            print(k, k*k, k**(fact[k]-3))
        continue
    if len(fact) == 2:
        a, b = list(fact.keys())
        if fact[a] >= 2 and fact[b] >= 2:
            print("YES")
            print(a, b, (a ** (fact[a] - 1)) * (b ** (fact[b] - 1)))
        elif fact[a] == 1 and fact[b] >= 3:
            print("YES")
            print(a, b, b ** (fact[b]-1))
        elif fact[b] == 1 and fact[a] >= 3:
            print("YES")
            print(a, b, a ** (fact[a]-1))
        else:
            print("NO")
        continue