Canadian Computing Competition: 2008 Stage 2, Day 2, Problem 2

You and a friend have a big bag of candy. You want to keep slim and trim, and so you would like to equalize the candy which you are sharing with your friend in terms of calorie count. That is, your task is to divide the candies into two groups such that the number of calories in each group is as close together as possible.

Input Specification

The first line of input contains the number of different kinds of candy you have in your bag of candy $N$ $(1\le N\le 100)$. On the following $N$ lines, there are pairs of numbers describing each type of candy. The candy description is of the form $k_i$ $c_i$ where $k_i$ is the number of that particular type of candy contained in the bag and $c_i$ is the calorie count for each piece of that type of candy. You may assume that $1\le k_i\le 500$ and $1\le c_i\le 200$.

Output Specification

Your output is one integer which is the minimum difference of calories between friends.

Sample Input

4
3 5
3 3
1 2
3 100

Sample Output

74

Explanation for Sample Output

Your friend takes two of the $100$-calorie candies, for a total of $200$ calories. You keep the remaining candies, which have $126$ calories.

Grading

You may assume that $50\mathrm{\%}$ of the test cases will have at $1\le N,k_i,c_i\le 100$. All test cases will have $1\le N\le 100$, $1\le k_i\le 500$ and $1\le c_i\le 200$.