1046 Shortest Distance (20 分)

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]), followed by $N$ integer distances D​1​​ D​2​​ ⋯ D​N​​, where D​i​​ is the distance between the $i$-th and the (-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 $M$ (≤), 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 1.

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:

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]), followed by $N$ integer distances D​1​​ D​2​​ ⋯ D​N​​, where D​i​​ is the distance between the $i$-th and the (-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 $M$ (≤), 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 1.

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: