Vika and Squares

题意翻译

Vika 有 $n$ 桶油漆，第 $i$ 桶有 $a_i$ 升油漆。 Vika 有一张无限长的长方形纸条，她将长方形纸条分成了无限个正方形，她将按照以下规则对正方形涂色。 - 涂一个正方形需要 $1$ 升油漆。 - 第一个正方形可以用第任意第 $i$ 桶油漆。 - 若第 $k$ 个正方形用了第 $x$ 桶油漆，则第 $k+1$ 个正方形将用第 $x+1$ 桶油漆，若 $x=n$，则第 $k+1$ 个正方形将用第 $1$ 桶油漆。若 $a_x = 0$ 则停止涂色。 求 Vika 最多可以涂多少个正方形。 # 输入格式： 两行 第 $1$ 行，一个整数 $n$。 第 $2$ 行，$n$ 个整数 $a_i$ 。 # 输出格式： 一行，Vika 最多可涂的正方形数量。 translate by @sqh_let_it_be

题目描述

Vika has $ n $ jars with paints of distinct colors. All the jars are numbered from $ 1 $ to $ n $ and the $ i $ -th jar contains $ a_{i} $ liters of paint of color $ i $ . Vika also has an infinitely long rectangular piece of paper of width $ 1 $ , consisting of squares of size $ 1×1 $ . Squares are numbered $ 1 $ , $ 2 $ , $ 3 $ and so on. Vika decided that she will start painting squares one by one from left to right, starting from the square number $ 1 $ and some arbitrary color. If the square was painted in color $ x $ , then the next square will be painted in color $ x+1 $ . In case of $ x=n $ , next square is painted in color $ 1 $ . If there is no more paint of the color Vika wants to use now, then she stops. Square is always painted in only one color, and it takes exactly $ 1 $ liter of paint. Your task is to calculate the maximum number of squares that might be painted, if Vika chooses right color to paint the first square.

输入输出格式

输入格式

The first line of the input contains a single integer $ n $ ( $ 1<=n<=200000 $ ) — the number of jars with colors Vika has. The second line of the input contains a sequence of integers $ a_{1},a_{2},...,a_{n} $ ( $ 1<=a_{i}<=10^{9} $ ), where $ a_{i} $ is equal to the number of liters of paint in the $ i $ -th jar, i.e. the number of liters of color $ i $ that Vika has.

输出格式

The only line of the output should contain a single integer — the maximum number of squares that Vika can paint if she follows the rules described above.

输入输出样例

输入样例 #1

5
2 4 2 3 3

输出样例 #1

12

输入样例 #2

3
5 5 5

输出样例 #2

15

输入样例 #3

6
10 10 10 1 10 10

输出样例 #3

11

说明

In the first sample the best strategy is to start painting using color $ 4 $ . Then the squares will be painted in the following colors (from left to right): 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5. In the second sample Vika can start to paint using any color. In the third sample Vika should start painting using color number $ 5 $ .