Denise is designing a rainforest themed board game. The goal of the game is for each player to form a team of two characters and complete various challenges.

There are $$$N$$$ different characters numbered from $$$1$$$ to $$$N$$$. Each character $$$i$$$ has two attributes $$$p_i$$$ and $$$s_i$$$ (problem solving skill and strength). The numbers $$$p_i$$$ and $$$s_i$$$ are positive integers satisfying $$$1 \leq p_i, s_i \leq N$$$. Before the game starts, each player will pick two characters $$$i$$$ and $$$j$$$ to form a team. It is possible to pick two copies of the same character. The total problem solving skill and strength of the team will be $$$p_i + p_j$$$ and $$$s_i + s_j$$$ respectively.

In the game there are also $$$N$$$ challenge cards numbered from $$$1$$$ to $$$N$$$. Each of these also has two attributes $$$P_k$$$ and $$$S_k$$$. Denise has already designed the challenge cards and decided on the values of all numbers $$$P_1, P_2, \dots, P_N$$$ and $$$S_1, S_2, \dots, S_N$$$. However, the rules of the game assume that it is not possible for a player to form a team whose problem solving skill and strength are both the same as one of the challenge cards. In other words, the situation

$$$$$$p_i+p_j = P_k \text{ and } s_i+s_j = S_k$$$$$$

should never occur for any triple $$$i,j,k$$$ (note that $$$i$$$ can be equal to $$$j$$$).

The only thing left to do is to decide the $$$N$$$ distinct pairs $$$(p_1, s_1), (p_2, s_2) \dots, (p_N, s_N)$$$ such that $$$1 \leq p_i, s_i \leq N$$$ and the situation above never happens.