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 i in range(0,t):
    n = int(input())
    a = 1
    j = 2
    while((j*j) <= n):
        if(n % j == 0):
            a = j
            break
        j = j + 1
    if(a == 1):
        print("NO")
    else:
        b = 1
        n = n / a
        j = a + 1
        while((j*j) <= n):
            if(n % j == 0):
                b = j
                break
            j = j + 1
        n = int(n / b)
        if(b == 1):
            print("NO")
        elif n <= b:
            print("NO")
        else:
            print("YES")
            print(str(a) + " " + str(b) + " " + str(n))