#1679. [Usaco2005 Jan]Moo Volume 牛的呼声

题目描述

Farmer John has received a noise complaint from his neighbor, Farmer Bob, stating that his cows are making too much noise. FJ's N cows (1 <= N <= 10,000) all graze at various locations on a long one-dimensional pasture. The cows are very chatty animals. Every pair of cows simultaneously carries on a conversation (so every cow is simultaneously MOOing at all of the N-1 other cows). When cow i MOOs at cow j, the volume of this MOO must be equal to the distance between i and j, in order for j to be able to hear the MOO at all. Please help FJ compute the total volume of sound being generated by all N*(N-1) simultaneous MOOing sessions.

约翰的邻居鲍勃控告约翰家的牛们太会叫．

约翰的N(1≤N≤10000)只牛在一维的草场上的不同地点吃着草．她们都是些爱说闲话的奶牛，每一只同时与其他N-1只牛聊着天．一个对话的进行，需要两只牛都按照和她们间距离等大的音量吼叫，因此草场上存在着N（N-1）/2个声音．  请计算这些音量的和．

输入格式

• Line 1: N * Lines 2..N+1: The location of each cow (in the range 0..1,000,000,000).

  第1行输入N，接下来输入N个整数，表示一只牛所在的位置．

输出格式

• Line 1: A single integer, the total volume of all the MOOs.

  一个整数，表示总音量．

样例

样例输入

5  

1  

5  

3  

2  

4  

  

INPUT DETAILS:  

  

There are five cows at locations 1, 5, 3, 2, and 4.  

样例输出

40  

  

OUTPUT DETAILS:  

  

Cow at 1 contributes 1+2+3+4=10, cow at 5 contributes 4+3+2+1=10, cow at 3  

contributes 2+1+1+2=6, cow at 2 contributes 1+1+2+3=7, and cow at 4  

contributes 3+2+1+1=7.  The total volume is (10+10+6+7+7) = 40.

数据范围与提示