The cows have opened a new business, and Farmer John wants to see how well they are doing. The business has been running for $N$ ($1 \leq N \leq 100{,}000$) days, and every day $i$ the cows recorded their net profit $P_i$ ($-1{,}000 \leq P_i \leq 1{,}000$).
Farmer John wants to find the largest total profit that the cows have made during any consecutive time period. (Note that a consecutive time period can range in length from one day through $N$ days.) Help him by writing a program to calculate the largest sum of consecutive profits.
Input
Read the input from standard input.
- Line 1: A single integer: $N$
- Lines $2..N+1$: Line $i+1$ contains a single integer: $P_i$
Output
Write the output to standard output.
- Line 1: A single integer representing the value of the maximum sum of profits for any consecutive time period.
Examples
Input 1
7 -3 4 9 -2 -5 8 -3
Output 1
14
The maximum sum is obtained by taking the sum from the second through the sixth number (4, 9, -2, -5, 8) => 14.
Problem credits: Neal Wu, 2007