Problem Statement

For positive integers x and y, define f(x, y) as the remainder of (x + y) divided by 10^8.
You are given a sequence of positive integers $A = (A_1, \ldots, A_N)$ of length N. Find the value of the following expression:
$\displaystyle \sum_{i=1}^{N-1}\sum_{j=i+1}^N f(A_i,A_j)$.

Input

The input is given from Standard Input in the following format:
N
$A_1 \ldots A_N$

Output

Print the answer.

Constraints

• $2 \leq N \leq 3\times 10^5$
• $1 \leq A_i < 10^8$
• All input values are integers.

Sample Input 1

3
3 50000001 50000002

Sample Output 1

100000012

• f(A_1,A_2)=50000004
• f(A_1,A_3)=50000005
• f(A_2,A_3)=3

Thus, the answer is f(A_1,A_2) + f(A_1,A_3) + f(A_2,A_3) = 100000012.
Note that you are not asked to compute the remainder of the sum divided by 10^8.

Sample Input 2

5
1 3 99999999 99999994 1000000

Sample Output 2

303999988

见题面 Input 部分

见题面 Output 部分