All Pair Digit Sums

AtCoder

IDarc158_c

Time4000ms

Memory256MB

Difficulty—

For a positive integer $x$, let $f(x)$ denote the sum of its digits. For instance, $f(158) = 1 + 5 + 8 = 14$, $f(2023) = 2 + 0 + 2 + 3 = 7$, and $f(1) = 1$. You are given a sequence of positive integers $A = (A_1, \ldots, A_N)$. Find $\sum_{i=1}^N\sum_{j=1}^N f(A_i + A_j)$. ## Constraints * $1\leq N\leq 2\times 10^5$ * $1\leq A_i < 10^{15}$ ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $\ldots$ $A_N$ [samples]

Samples

Input #1

2
53 28

Output #1

36

We have $\sum_{i=1}^N\sum_{j=1}^N f(A_i + A_j) = f(A_1+A_1)+f(A_1+A_2)+f(A_2+A_1)+f(A_2+A_2)=7+9+9+11=36$.

Input #2

1
999999999999999

Output #2

135

We have $\sum_{i=1}^N\sum_{j=1}^N f(A_i + A_j) = f(A_1+A_1) = 135$.

Input #3

5
123 456 789 101 112

Output #3

API Response (JSON)

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  "problem": {
    "name": "All Pair Digit Sums",
    "description": {
      "content": "For a positive integer $x$, let $f(x)$ denote the sum of its digits. For instance, $f(158) = 1 + 5 + 8 = 14$, $f(2023) = 2 + 0 + 2 + 3 = 7$, and $f(1) = 1$. You are given a sequence of positive intege",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
    },
    "difficulty": "None",
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    "is_sync": true,
    "sync_url": null,
    "sign": "arc158_c"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "For a positive integer $x$, let $f(x)$ denote the sum of its digits. For instance, $f(158) = 1 + 5 + 8 = 14$, $f(2023) = 2 + 0 + 2 + 3 = 7$, and $f(1) = 1$.\nYou are given a sequence of positive intege...",
      "is_translate": false,
      "language": "English"
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