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 
def sol(n):
    ans = []
    i = 2
    cnt = 0
    while n > 0 and i*i <= n:
        if not(n%i):
            cnt += 1
            n //= i
            ans.append(i)
        i += 1
        if cnt >= 2:
            break
    tr = cnt >= 2 and n not in ans
    print("YES" if tr else "NO")
    if tr:
        print(*ans[:2], n)
    

t = int(input())

for _ in range(t):
    n = int(input())
    res = sol(n)
