Splitting Pile

Snuke and Raccoon have a heap of N cards. The i-th card from the top has the integer a_i written on it.

They will share these cards. First, Snuke will take some number of cards from the top of the heap, then Raccoon will take all the remaining cards. Here, both Snuke and Raccoon have to take at least one card.

Let the sum of the integers on Snuke's cards and Raccoon's cards be x and y, respectively. They would like to minimize |x-y|. Find the minimum possible value of |x-y|.

Constraints

• 2 \leq N \leq 2 \times 10^5
• -10^{9} \leq a_i \leq 10^{9}
• a_i is an integer.

Input

Input is given from Standard Input in the following format:

N a_1 a_2 ... a_{N}

Output

Print the answer.

Examples

Input

6 1 2 3 4 5 6

Output

1

Input

2 10 -10

Output

20

inputFormat

Input

Input is given from Standard Input in the following format:

N a_1 a_2 ... a_{N}

outputFormat

Output

Print the answer.

Examples

Input

6 1 2 3 4 5 6

Output

1

Input

2 10 -10

Output

20

样例

6
1 2 3 4 5 6

1