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<h1>1046. Shortest Distance (20)</h1>
<div id="problemContent">
<p>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.</p>
<p><b>
Input Specification:
</b></p>
<p>Each input file contains one test case. For each case, the first line contains an integer N (in [3, 10<sup>5</sup>]), followed by N integer distances D<sub>1</sub> D<sub>2</sub> ... D<sub>N</sub>, where D<sub>i</sub> is the distance between the i-th and the (i+1)-st exits, and D<sub>N</sub> 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 (&lt;=10<sup>4</sup>), 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<sup>7</sup>.</p>
<p><b>
Output Specification:
</b></p>
<p>For each test case, print your results in M lines, each contains the shortest distance between the corresponding given pair of exits.</p>
<b>Sample Input:</b><pre>
5 1 2 4 14 9
3
1 3
2 5
4 1
</pre>
<b>Sample Output:</b><pre>
3
10
7
</pre>
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