Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Geometry Horse

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputVasya plays the Geometry Horse.

The game goal is to destroy geometric figures of the game world. A certain number of points is given for destroying each figure depending on the figure type and the current factor value.

There are *n* types of geometric figures. The number of figures of type *k*_{i} and figure cost *c*_{i} is known for each figure type. A player gets *c*_{i}·*f* points for destroying one figure of type *i*, where *f* is the current factor. The factor value can be an integer number from 1 to *t* + 1, inclusive. At the beginning of the game the factor value is equal to 1. The factor is set to *i* + 1 after destruction of *p*_{i} (1 ≤ *i* ≤ *t*) figures, so the (*p*_{i} + 1)-th figure to be destroyed is considered with factor equal to *i* + 1.

Your task is to determine the maximum number of points Vasya can get after he destroys all figures. Take into account that Vasya is so tough that he can destroy figures in any order chosen by him.

Input

The first line contains the only integer number *n* (1 ≤ *n* ≤ 100) — the number of figure types.

Each of the following *n* lines contains two integer numbers *k*_{i} and *c*_{i} (1 ≤ *k*_{i} ≤ 10^{9}, 0 ≤ *c*_{i} ≤ 1000), separated with space — the number of figures of the *i*-th type and the cost of one *i*-type figure, correspondingly.

The next line contains the only integer number *t* (1 ≤ *t* ≤ 100) — the number that describe the factor's changes.

The next line contains *t* integer numbers *p*_{i} (1 ≤ *p*_{1} < *p*_{2} < ... < *p*_{t} ≤ 10^{12}), separated with spaces.

Please, do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specificator.

Output

Print the only number — the maximum number of points Vasya can get.

Examples

Input

1

5 10

2

3 6

Output

70

Input

2

3 8

5 10

1

20

Output

74

Note

In the first example Vasya destroys three figures first and gets 3·1·10 = 30 points. Then the factor will become equal to 2 and after destroying the last two figures Vasya will get 2·2·10 = 40 points. As a result Vasya will get 70 points.

In the second example all 8 figures will be destroyed with factor 1, so Vasya will get (3·8 + 5·10)·1 = 74 points.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Feb/20/2019 15:40:29 (d3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|