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:
t = int(input())
for _ in range(t):
    n = num = int(input())
    arr = []
    div = 2
    while n != 1:
        if div > int(n**0.5):
            arr.append(n)
            n //= div
            break

        if n % div == 0:
            n //= div
            arr.append(div)
            continue
        div += 1

    if len(arr) < 3:
        print("NO")
    else:
        cand = []
        cur = 1
        while arr:
            cur *= arr.pop(0)
            if cur not in cand:
                cand.append(cur)
                cur = 1
        if cur != 1:
            cand[-1] *= cur

        if len(cand) < 3:
            print("NO")
        else:
            while len(cand) != 3:
                cur = cand.pop()
                cand[-1] *= cur
            print("YES")
            print(*cand)


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