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:
# maa chudaaye duniya
import math
def pf(n):
    cat = []
    while n%2 == 0:
        cat.append(2)
        n //= 2
    for i in range(3, int(math.sqrt(n)) + 1, 2):
        while n%i == 0:
            cat.append(i)
            n //= i
    if n > 2:
        cat.append(n)
    return cat

for _ in range(int(input())):
    n = int(input())
    factors = pf(n)
    factors.sort()
    ss = list(set(factors))
    # print(factors)
    if len(ss) >= 3 and len(factors) >= 3:
        a = ss[0]
        b = ss[1]
        d = a*b
        c = n // d
        print('YES')
        print(a, b, c)
    elif len(ss) == 1 and len(factors) >= 6:
        a = ss[0]
        b = pow(a, 2)
        c = n // pow(a, 3)
        print('YES')
        print(a, b, c)
    elif len(ss) == 2 and len(factors) >= 4:
        a = ss[0]
        b = ss[1]
        c = n // (a*b)
        print('YES')
        print(a, b, c)
    else:
        print('NO')