The task is really simple: given N exits on a highway which forms a simple cycle, you are supposed to tell the shortest distance between any pair of exits.

Input Specification:

Each input file contains one test case. For each case, the first line contains an integer N (in [3,10​5​​]), followed by N integer distances D​1​​ D​2​​ ⋯ D​N​​, where D​i​​ is the distance between the i-th and the (i+1)-st exits, and D​N​​ is between the N-th and the 1st exits. All the numbers in a line are separated by a space. The second line gives a positive integer M (≤10​4​​), with M lines follow, each contains a pair of exit numbers, provided that the exits are numbered from 1 to N. It is guaranteed that the total round trip distance is no more than 10​7​​.

Output Specification:

For each test case, print your results in M lines, each contains the shortest distance between the corresponding given pair of exits.

Sample Input:

5 1 2 4 14 9
3
1 3
2 5
4 1

Sample Output:

3
10
7

一道典型的前缀和的问题，如果存储到相邻两个节点的距离，计算两点之间距离需要遍历相加，这样会超时

从第一个节点开始，每个节点纪录到最前面的距离之和，查询的时候直接相减就好了。

如图所示，如果要计算1-3，顺序dis=data[3-1]-data[1-1]，即data[2]-data[0]，

                                             反序rdis=data[5]-data[3-1]+data[1-1]，即data[5]-data[2]+data[0];