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:
#right preference 
q = int(input())
for rwre in range(q):
    n = int(input())
    dz = []
    nn = n
    kan = 2
    while nn > 1 and kan**2 <= n:
        if nn%kan == 0:
            nn//= kan
            dz.append(kan)
        else:
            kan += 1
    if nn > 1:
        dz.append(nn)
    dz.append(52525425542542)
    roz = []
    for i in range(1,len(dz)):
        if dz[i] != dz[i-1]:
            roz.append(dz[i-1])
    dz.pop(-1)
    if len(roz) >= 3:
        print("YES")
        print(roz[0],roz[1],n//(roz[0]*roz[1]))
    else:
        if len(roz) == 1:
            a = roz[0]
            b = roz[0]**2
            c = n//(roz[0]**3)
            if c > 1 and c != b and c != a:
                print("YES")
                print(a,b,c)
            else:
                print("NO")
        if len(roz) == 2:
            c = n//(roz[1]*roz[0])
            if c != roz[1] and c!= roz[0] and c > 1:
                print("YES")
                print(roz[0],roz[1],c)
            else:
                print("NO")