4863: Product Sum
内存限制：256 MB
时间限制：2 S
标准输入输出
题目类型：传统
评测方式：文本比较
上传者：
提交：2
通过：1
题目描述
E. Product Sum
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
Blake is the boss of Kris, however, this doesn't spoil their friendship. They often gather at the bar to talk about intriguing problems about maximising some values. This time the problem is really special.
You are given an array a of length n. The characteristic of this array is the value
− the sum of the products of the values ai by i. One may perform the following operation exactly once: pick some element of the array and move to any position. In particular, it's allowed to move the element to the beginning or to the end of the array. Also, it's allowed to put it back to the initial position. The goal is to get the array with the maximum possible value of characteristic.
You are given an array a of length n. The characteristic of this array is the value
− the sum of the products of the values ai by i. One may perform the following operation exactly once: pick some element of the array and move to any position. In particular, it's allowed to move the element to the beginning or to the end of the array. Also, it's allowed to put it back to the initial position. The goal is to get the array with the maximum possible value of characteristic.
Input
The first line of the input contains a single integer n (2≤n≤200000)− the size of the array a. The second line contains n integers ai (1≤i≤n, |ai|≤1000000)− the elements of the array a.
Output
Print a single integer − the maximum possible value of characteristic of a that can be obtained by performing no more than one move.
Examples
Input
4 4 3 2 5
Output
39
Input
5 1 1 2 7 1
Output
49
Input
3 1 1 2
Output
9
Note
In the first sample, one may pick the first element and place it before the third (before 5). Thus, the answer will be 3·1+2·2+4·3+5·4=39. In the second sample, one may pick the fifth element of the array and place it before the third. The answer will be 1·1+1·2+1·3+2·4+7·5=49.
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