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 solve():
    n = int(input())
    primes = {}
    i = 2
    while i * i <= n:
        while n % i == 0:
            primes[i] = primes.get(i, 0) + 1
            n //= i
        i += 1
    if n > 1:
        primes[n] = primes.get(n, 1)
    k = list(primes.keys())
    v = list(primes.values())
    if len(primes) >= 3:
        print("YES")
        print(k[0] ** primes[k[0]], k[1] ** primes[k[1]], end=' ')
        third = 1
        for i in range(2, len(k)):
            third *= k[i] ** primes[k[i]]
        print(third)
    else:
        if len(primes) == 1:
            if sum(v) >= 6:
                print("YES")
                print(k[0], k[0] ** 2, k[0] ** (v[0] - 3))
            else:
                print("NO")
        elif len(primes) == 2:
            if v[0] <= 1 and v[1] <= 1:
                print("NO")
            elif (v[0] == 1 and v[1] == 2) or (v[0] == 2 and v[1] == 1):
                print("NO")
            else:
                print("YES")
                print(k[0], k[1], k[0] ** (v[0] - 1) * k[1] ** (v[1] - 1))


t = int(input())
while t > 0:
    solve()
    t -= 1