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:
prime = []
l = []
for i in range(40000):
    prime.append(True)
for i in range(2,40000):
    if prime[i] == True:
        l.append(i)
        tmp = 2*i
        while tmp < 40000:
            prime[tmp] = False
            tmp += i

t = int(input())
for i in range(t):
    n = int(input())
    flag = False
    for j in l:
        if j**2 > n:
            break
        if n%j == 0:
            q = n//j
            for k in range(j+1, q):
                if k**2 > q:
                    break
                if k != j and q%k == 0:
                    if q//k != k:
                        flag = True
                        print("YES")
                        print(j, k, q//k, sep = " ")
                    break
            break
    if flag == False:
        print("NO")