Sum Balance

Description:

Input:

The first line contains a single integer $$$k$$$ ($$$1 \leq k \leq 15$$$), the number of boxes.

The $$$i$$$-th of the next $$$k$$$ lines first contains a single integer $$$n_i$$$ ($$$1 \leq n_i \leq 5\,000$$$), the number of integers in box $$$i$$$. Then the same line contains $$$n_i$$$ integers $$$a_{i,1}, \ldots, a_{i,n_i}$$$ ($$$|a_{i,j}| \leq 10^9$$$), the integers in the $$$i$$$-th box.

It is guaranteed that all $$$a_{i,j}$$$ are distinct.

Output:

If Ujan cannot achieve his goal, output "No" in a single line. Otherwise in the first line output "Yes", and then output $$$k$$$ lines. The $$$i$$$-th of these lines should contain two integers $$$c_i$$$ and $$$p_i$$$. This means that Ujan should pick the integer $$$c_i$$$ from the $$$i$$$-th box and place it in the $$$p_i$$$-th box afterwards.

If there are multiple solutions, output any of those.

You can print each letter in any case (upper or lower).

Sample Input:

4
3 1 7 4
2 3 2
2 8 5
1 10

Sample Output:

Yes
7 2
2 3
5 1
10 4

Sample Input:

2
2 3 -2
2 -1 5

Sample Output:

No

Sample Input:

2
2 -10 10
2 0 -20

Sample Output:

Yes
-10 2
-20 1

Note:

In the first sample, Ujan can put the number $$$7$$$ in the $$$2$$$nd box, the number $$$2$$$ in the $$$3$$$rd box, the number $$$5$$$ in the $$$1$$$st box and keep the number $$$10$$$ in the same $$$4$$$th box. Then the boxes will contain numbers $$$\{1,5,4\}$$$, $$$\{3, 7\}$$$, $$$\{8,2\}$$$ and $$$\{10\}$$$. The sum in each box then is equal to $$$10$$$.

In the second sample, it is not possible to pick and redistribute the numbers in the required way.

In the third sample, one can swap the numbers $$$-20$$$ and $$$-10$$$, making the sum in each box equal to $$$-10$$$.