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:
#C
for _ in range(int(input())):
    n = int(input())
    cnt=0
    ans = []
    for i in range(2,int(n**0.5)+1):
        if n % i == 0:
            cnt+=1
            ans.append(i)
        if cnt == 2 and n % (ans[0]*ans[1]) == 0 and n//(ans[0]*ans[1]) != ans[0] and n//(ans[0]*ans[1]) != ans[1]:
            break
        if cnt == 2 and n % (ans[0]*ans[1]) != 0:
            del ans[1]
            cnt-=1
    if cnt == 2:
        if n % (ans[0]*ans[1]) == 0 and n//(ans[0]*ans[1]) != ans[0] and n//(ans[0]*ans[1]) != ans[1]:
            ans.append(n//(ans[0]*ans[1]))
    #print(ans)
    if len(ans)==3:
        print('YES')
        print(*ans)
    else:
        print('NO')