Problem A
Bootfall

After the latest World Cup, some countries are considering withdrawing from FIFA and forming a new sport: bootfall. In bootfall, two teams with $N$ players each compete. A player can be either a defender or an attacker, and before each match, the team gets to decide which role each player will have.

You are the coach of a team with $N$ players, where the $i$-th player has an attack level $a_i$ and a defense level $d_i$. The team’s attack strength $A$ is the sum of all $a_i$ of the players who are attackers, and the team’s defense strength $D$ is the sum of $d_i$ of those who are defenders. If the team faces another team with attack strength $A'$ and defense strength $D'$, your team will score $\max (0, A-D')$ goals, while the opposing team will score $\max (0, A'-D)$ goals.

Your team will face $Q$ other teams, where the $i$-th team has attack strength $A_i$ and defense strength $D_i$. Your task is to decide for each match who should defend and who should attack to achieve the best possible result (ideally, you want to win, then draw, and preferably not lose).

Input

The first line contains the integer $N$ ($1 \leq N \leq 400$), the number of players on your team.

The following $N$ lines contain two integers $a_i$ and $d_i$ ($0 \leq a_i, d_i \leq 400$), the attack strength and defense strength of player $i$.

The next line contains an integer $Q$ ($1 \leq Q \leq 3 \cdot 10^5$), the number of matches.

Then follow $Q$ lines, each containing two integers $A_i$ and $D_i$ ($0 \leq A_i, D_i \leq 160000$), which means that your team faces a team with attack strength $A_i$ and defense strength $D_i$.

Output

Print three integers $w$, $d$, $l$ on a single line: the number of matches you will win, tie, and lose, if you optimally choose who will defend and attack each game.

Scoring

Your solution will be tested on a set of test groups, each worth a number of points. Each test group contains a set of test cases. To get the points for a test group you need to solve all test cases in the test group.

4
2 3
1 1
0 2
5 1
5
5 5
6 5
7 10
10 0
12 0

2 2 1