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Robot

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You have two arrays of integers, and , where both have number of elements. Consider the following function:

score = 0

int Go(step, energy) {
    if (step == N) {
        score += V[step];
        return (score);
    }
    else {
        int way = random(1, 2);
        if (way == 1) {
            score += V[step];
        }
        else {
            energy = P[step];
        }
        if (energy > 0) {
            Go(step + 1, energy - 1);
        }
        else {
            KillTheWorld();
        }
    }
}

What is the maximum possible value of score that we can get in the end, if we call ?.
Note that the function should never invoke KillTheWorld function. And generates a random integer from set [1, 2].
It is guaranteed there will be a solution that wont kill the world.

Input Format

The first line contains an integer N. Each of the following N lines contains a pair of integers. The i-th line contains a pair of numbers, , separated by space.

Constraints



Output Format

Derive the maximum score given by return (score);.

Sample Input

4
4 2
0 2
4 0
3 4

Sample Output

7

Explanation

In the best case, the first and second function call in Go variable will take value 2, while in the other calls it will be equal to 1 then the final score will be equal to the value of 7.

Author

vlade087

Difficulty

Advanced

Max Score

120

Submitted By

1540

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