Sum of Sum of Digits

AtCoder

IDarc153_d

Time5000ms

Memory256MB

Difficulty—

For a positive integer $x$, let $f(x)$ denote the sum of its digits. For instance, we have $f(153) = 1 + 5 + 3 = 9$, $f(2023) = 2 + 0 + 2 + 3 = 7$, and $f(1) = 1$. You are given a sequence of positive integers $A = (A_1, \ldots, A_N)$. Find the minimum possible value of $\sum_{i=1}^N f(A_i + x)$ where $x$ is a non-negative integer. ## Constraints * $1\leq N\leq 2\times 10^5$ * $1\leq A_i < 10^9$ ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $\ldots$ $A_N$ [samples]

Samples

Input #1

4
4 13 8 6

Output #1

14

For instance, $x = 7$ makes $\sum_{i=1}^N f(A_i+x) = f(11) + f(20) + f(15) + f(13) = 14$.

Input #2

4
123 45 678 90

Output #2

34

For instance, $x = 22$ makes $\sum_{i=1}^N f(A_i+x) = f(145) + f(67) + f(700) + f(112) = 34$.

Input #3

3
1 10 100

Output #3

3

For instance, $x = 0$ makes $\sum_{i=1}^N f(A_i+x) = f(1) + f(10) + f(100) = 3$.

Input #4

1
153153153

Output #4

1

For instance, $x = 9999846846847$ makes $\sum_{i=1}^N f(A_i+x) = f(10000000000000) = 1$.

API Response (JSON)

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  "problem": {
    "name": "Sum of Sum of Digits",
    "description": {
      "content": "For a positive integer $x$, let $f(x)$ denote the sum of its digits. For instance, we have $f(153) = 1 + 5 + 3 = 9$, $f(2023) = 2 + 0 + 2 + 3 = 7$, and $f(1) = 1$. You are given a sequence of positive",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 5000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc153_d"
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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, we have $f(153) = 1 + 5 + 3 = 9$, $f(2023) = 2 + 0 + 2 + 3 = 7$, and $f(1) = 1$.\nYou are given a sequence of positive...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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