Maximize Total Area of Rectangles (SDE 2)

Each stick may go unused or be used in at most one rectangle, and each stick's length can be reduced by at most 1 but never increased. Each rectangle must use four sticks forming two pairs of equal sides; a square is also valid. First maximize the total area of all rectangles, then take it modulo 1000000007.

输入格式

The first line contains n; the second line contains the stick lengths. 1≤n≤100000, 2≤length≤10000.

输出格式

Output a single integer, the answer.

样例 1

输入：

6
2 6 2 6 3 5

输出：

12

样例 2

输入：

8
2 3 3 4 6 8 8 6

输出：

54

样例 3

输入：

5
3 4 5 5 6

输出：

20

样例说明

The answers are 12, 54 and 20. In the third example 6 and 5 pair up as 5, and the other 5 and 4 pair up as 4, for area 20.