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 IsPrime(n):
   d = 2
   while d * d <= n and n % d != 0:
       d += 1
   return d * d > n

t = int(input())
ans = []
for j in range(t):
    n = int(input())
    divs = []
    i = 2
    while i*i <= n:
        if n % i == 0:
            x = n // i
            u = i + 1
            while u*u <= x:
                if x % u == 0:
                    if x//u == u:
                        break
                    ans.append(['YES', i, u, x//u])
                    u = x
                    i = n
                u += 1
        i +=1
    if len(ans) == j:
        ans.append(['NO'])
for i in range(len(ans)):
    if len(ans[i]) == 1:
        print(*ans[i])
    else:
        print(ans[i][0])
        print(*ans[i][1::])