Mirko got an array of integers for his birthday from his grandmother Norma. As any other kid, he was hoping for some money, but got an array. Luckily, in his town there is a pawn shop that buys up arrays. The cost of an array of integers is min·max·L kunas, where min is the minimal integer in the array, max is the maximal and L is the array length. Mirko is going to sell a subsequence of consecutive numbers from his array. He calculated the average price of all such subsequences.

In order to check his result, he wants you to do the same. He will be pleased with only the last 9 digits of the sum of all prices, so you don’t need to bother with large and real numbers.

SCORING

입력

• The first line of input contains an integer N (1 <= N <= 500 000).
• Each of the following N lines contains a member of Mirko’s array. The members of the array will be integers from the interval [1, 10^8 ].

출력

입출력 예

입력

2
1
3

출력

16 

입력

4
2
4
1
4

출력

109 

입력

6
8
1
3
9
7
4

출력

1042

Clarification of the first example: The array consists of two integers, 1 and 3. The possible subsequences Mirko can
sell are (1), (3) and (1,3), their prices being 1, 9 and 6, respectively, which is 16 summed up. Clarification of the second
example: The possible subsequences Mirko can sell are (2), (4), (1), (4), (2, 4), (4, 1), (1, 4), (2,4,1), (4,1,4) and (2,4,1,4).
Their prices are 4, 16, 1, 16, 16, 8, 8, 12, 12 and 16, respectively, which is 109 summed up.

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