Problem: You are given three positive (i.e. strictly greater than zero) integers x, y and z.

Your task is to find positive integers a, b and c such that x = max(a, b), y = max(a, c) and z = max(b, c), or determine that it is impossible to find such a, b and c.

You have to answer t independent test cases. Print required a, b and c in any (arbitrary) order.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow.

The only line of the test case contains three integers x, y, and z (1 ≤ x, y, z ≤ 10^9).

Output

For each test case, print the answer:

  * "NO" in the only line of the output if a solution doesn't exist; 
  * or "YES" in the first line and any valid triple of positive integers a, b and c (1 ≤ a, b, c ≤ 10^9) in the second line. You can print a, b and c in any order. 

Example

Input


5
3 2 3
100 100 100
50 49 49
10 30 20
1 1000000000 1000000000


Output


YES
3 2 1
YES
100 100 100
NO
NO
YES
1 1 1000000000

Solution (in PYTHON3):

Solution:
def f(x,y,z):
    a=x
    if y<x:
        return False
    if y==x:
        if x<z:
            return False
        else:
            c,b=z,z
            return True,a,b,c
    if y>x:
        c=y
        if y==z:
            b=1
            return True,a,b,c
        if y>z:
            return False
        if y<z:
            if x>=z:
                b=z
                return True,a,b,c
            else:
                return False


for t in range(int(input())):
    x,y,z=map(int,input().strip().split())
    if f(x,y,z)==False:
        if f(x,z,y)==False:
            print("NO")
        else:
            s,m,l,p=f(x,z,y)
            print("YES")
            print(m,l,p)
    else:
        print("YES")
        s,m,l,p=f(x,y,z)
        print(m,l,p)