Three Pairwise Maximums

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

inputFormat

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).

outputFormat

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

样例

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

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

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