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:
import sys
input = sys.stdin.readline

t = int(input())
for _ in range(t):
    inputs = [int(x) for x in input().split()]
    value_counts = {}
    for x in inputs:
        if x in value_counts:
            value_counts[x] += 1
        else:
            value_counts[x] = 1
    if len(value_counts) == 3:
        print("NO")
    if len(value_counts) == 2:
        minv = min(list(value_counts.keys()))
        maxv = max(list(value_counts.keys()))
        if value_counts[minv] == 1:
            print("YES")
            out_string = ""
            out_string += str(minv) + " "
            out_string += str(maxv) + " "
            out_string += str(minv)
            print(out_string)
        else:
            print("NO")
    if len(value_counts) == 1:
        val = list(value_counts.keys())[0]
        print("YES")
        out_string = (str(val) + " ")*2 + str(val)
        print(out_string)