Sigma Problem

AtCoder

IDabc353_c

Time2000ms

Memory256MB

Difficulty—

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: $\displaystyle \sum_{i=1}^{N-1}\sum_{j=i+1}^N f(A_i,A_j)$. ## Constraints * $2 \leq N \leq 3\times 10^5$ * $1 \leq A_i < 10^8$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $\ldots$ $A_N$ [samples]

Samples

Input #1

3
3 50000001 50000002

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 $10^8$.

Input #2

5
1 3 99999999 99999994 1000000

Output #2

303999988

API Response (JSON)

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    "name": "Sigma Problem",
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      "content": "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 valu",
      "description_type": "Markdown"
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    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
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    "difficulty": "None",
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    {
      "statement_type": "Markdown",
      "content": "For positive integers $x$ and $y$, define $f(x, y)$ as the remainder of $(x + y)$ divided by $10^8$.\nYou are given a sequence of positive integers $A = (A_1, \\ldots, A_N)$ of length $N$. Find the valu...",
      "is_translate": false,
      "language": "English"
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