Polycarpus has a complex electronic device. The core of this device is a circuit board. The board has 10^9 contact points which are numbered from 1 to 10^9. Also there are n wires numbered from 1 to n, each connecting two distinct contact points on the board. An electric signal can pass between wires A and B if: 

  * either both wires share the same contact point; 
  * or there is a sequence of wires starting with A and ending with B, and each pair of adjacent wires in the sequence share a contact point. 

<image> The picture shows a circuit board with 5 wires. Contact points with numbers 2, 5, 7, 8, 10, 13 are used. Here an electrical signal can pass from wire 2 to wire 3, but not to wire 1.

Currently the circuit board is broken. Polycarpus thinks that the board could be fixed if the wires were re-soldered so that a signal could pass between any pair of wires.

It takes 1 minute for Polycarpus to re-solder an end of a wire. I.e. it takes one minute to change one of the two contact points for a wire. Any contact point from range [1, 10^9] can be used as a new contact point. A wire's ends must always be soldered to distinct contact points. Both wire's ends can be re-solded, but that will require two actions and will take 2 minutes in total.

Find the minimum amount of time Polycarpus needs to re-solder wires so that a signal can pass between any pair of wires. Also output an optimal sequence of wire re-soldering.

Input

The input contains one or several test cases. The first input line contains a single integer t — number of test cases. Then, t test cases follow.

The first line of each test case contains a single integer n (1 ≤ n ≤ 10^5) — the number of wires. The following n lines describe wires, each line containing two space-separated integers x_i, y_i (1 ≤ x_i, y_i ≤ 10^9, x_i ≠ y_i) — contact points connected by the i-th wire. A couple of contact points can be connected with more than one wire.

Sum of values of n across all test cases does not exceed 10^5.

Output

For each test case first print one line with a single integer k — the minimum number of minutes needed to re-solder wires so that a signal can pass between any pair of wires. In the following k lines print the description of re-solderings. Each re-soldering should be described by three integers w_j, a_j, b_j (1 ≤ w_j ≤ n, 1 ≤ a_j, b_j ≤ 10^9). Such triple means that during the j-th re-soldering an end of the w_j-th wire, which was soldered to contact point a_j, becomes soldered to contact point b_j instead. After each re-soldering of a wire it must connect two distinct contact points. If there are multiple optimal re-solderings, print any of them.

Example

Input


2
1
4 7
4
1 2
2 3
4 5
5 6


Output


0
1
2 3 5

Source: codeforces | Difficulty: HARD
Tags: Graph algorithms

Graph traversal

Greedy algorithms


Solutions: