Banquet Preparations 2

Description:

Input:

The first line of input data contains an integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases.

Each test case's description is preceded by a blank line. Next comes a line that contains an integer $$$n$$$ ($$$1 \leq n \leq 2 \cdot 10^5$$$) — the number of dishes. Then follows $$$n$$$ lines, $$$i$$$-th of which contains three integers $$$a_i$$$, $$$b_i$$$ and $$$m_i$$$ ($$$0 \leq a_i, b_i \le 10^6$$$; $$$0 \le m_i \le a_i+b_i$$$) — the mass of fish in $$$i$$$-th dish, the mass of meat in $$$i$$$-th dish and how many grams in total the taster should eat in $$$i$$$-th dish.

The sum of all $$$n$$$ values for all input data sets in the test does not exceed $$$2 \cdot 10^5$$$.

Output:

For each test case, print on the first line the minimum value of variety that can be achieved by eating exactly $$$m_i$$$ grams of food (for all $$$i$$$ from $$$1$$$ to $$$n$$$) from a dish $$$i$$$.

Then print $$$n$$$ lines that describe a way to do this: the $$$i$$$-th line should contain two integers $$$x_i$$$ and $$$y_i$$$ ($$$0 \leq x_i \leq a_i$$$; $$$0 \leq y_i \leq b_i$$$; $$$x_i+y_i=m_i$$$), where $$$x_i$$$ is how many grams of fish the taster should eat from $$$i$$$-th dish, and $$$y_i$$$ is how many grams of meat.

If there are several ways to achieve a minimum balance, print any of them.

Sample Input:

5

3
10 10 2
9 9 0
10 9 1

2
3 4 1
5 1 2

3
7 2 5
6 5 4
5 5 6

1
13 42 50

5
5 7 12
3 1 4
7 3 7
0 0 0
4 1 5

Sample Output:

1
1 1
0 0
1 0
2
0 1
1 1
2
3 2
0 4
1 5
1
8 42
2
5 7
3 1
4 3
0 0
4 1