Practice Linear algebra and Two pointers with the exercise "1000000000D WORLD"

Statement

Goal

You are in 1000000000D World!
In 1000000000D World all vectors consist of exactly one billion integers.

People of 1000000000D World are quite smart and they know that due to low entropy and "curse of dimensionality" most of their billion-dimensional vectors have a lot of consequent repetitions. So they always store their vectors in a compressed form.


For example consider a vector in canonical form: 

[1 1 1 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 ... (999999995 times 3)]

In compressed form it will become just:

[3 1 2 2 999999995 3]    (which stands for 3 times 1 and 2 times 2 and 999999995 times 3)

Given two 1000000000D vectors A and B in compressed form.
Find a dot product of two vectors

Dot product definition:
For two vectors a = [a_1 a_2 ... a_n] and b = [b_1 b_2 ... b_n] dot product "a • b" = a_1 * b_1 + a_2 * b_2 + ... + a_n * b_n

Input

Line 1 Compressed Vector A
Line 2 Compressed Vector B

Output

Dot product of A and B

Constraints

The absolute values of the final result and all intermediate results are less than 2^40

Example

Input

500000001 1 499999999 -1
1000000000 1

Output

Solve it

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