Simple calculations

Time Limit: 1000MS

Memory Limit: 65536K

Description

There is a sequence of n+2 elements a0, a1, ..., an+1 (n <= 3000, -1000 <= ai <=1000). It is known that ai = (ai-1 + ai+1)/2 - ci for each i=1, 2, ..., n. You are given a0, an+1, c1, ... , cn. 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 an+1 each having two digits after decimal point, and the next n lines contain numbers ci (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 an+1.

Sample Input

1
50.50
25.50
10.15

Sample Output

27.85

Hint

Source

N/A

提交代码