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 primfacs(n):
    i = 2
    primfac = []
    while i * i <= n:
        while n % i == 0:
            primfac.append(i)
            n = n / i
        i = i + 1
    if n > 1:
        primfac.append(n)
    return primfac


def mul(arr):
    p = 1
    if not len(arr):
        return 0
    for i in arr:
        p = p * i
    return p

t = int(input())
for _ in range(t):
    n = int(input())
    dels = primfacs(n)
    result = [dels[0]]
    tmp = []
    for i in range(1, len(dels)):
        tmp.append(dels[i])
        p = mul(tmp)
        if not p or p in result:
            continue
        else:
            if len(result) < 2:
                result.append(p)
                tmp = []
            else:
                continue
    p = mul(tmp)
    if not p or p in result:
        print("NO")
    else:
        result.append(p)
        print("YES")
        print(' '.join(str(int(i)) for i in result))