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 all_same(x, y, z):
    if x==y and y==z and x==z:
        return 1
    return 0

def analyze(x, y, z):
    if x==y and x>z:
        return 1
    elif x==z and x>y:
        return 1
    elif y==z and x<y:
        return 1
    else:
        return 0

for case in range(int(input())):
    x, y, z = map(int, input().split())
    if all_same(x, y, z)==True:
        print("YES")
        print(x, y, z)
    elif analyze(x, y, z)==True:
        print("YES")
        print(max(x, y, z), min(x, y, z), 1)
    else:
        print("NO")