Description

There is a sequence of n+2 elements a₀, a₁, ..., a_n+1 (n <= 3000, -1000 <= a_i <=1000). It is known that a_i = (a_i-1 + a_i+1)/2 - c_i for each i=1, 2, ..., n.

You are given a₀, a_n+1, c₁, ... , c_n. Write a program which calculates a₁.

Input

The first line of an input contains an integer n. The next two lines consist of numbers a₀ and a_n+1 each having two digits after decimal point, and the next n lines contain numbers c_i (also with two digits after decimal point), one number per line.

Output

The output file should contain a₁ in the same format as a₀ and a_n+1.

1
50.50
25.50
10.15

27.85

Source

Ural State University collegiate programming contest 2000