Modulo Summation

AtCoder

IDabc103_c

Time2000ms

Memory256MB

Difficulty—

You are given $N$ positive integers $a_1, a_2, ..., a_N$. For a non-negative integer $m$, let $f(m) = (m\ mod\ a_1) + (m\ mod\ a_2) + ... + (m\ mod\ a_N)$. Here, $X\ mod\ Y$ denotes the remainder of the division of $X$ by $Y$. Find the maximum value of $f$. ## Constraints * All values in input are integers. * $2 \leq N \leq 3000$ * $2 \leq a_i \leq 10^5$ ## Input Input is given from Standard Input in the following format: $N$ $a_1$ $a_2$ $...$ $a_N$ [samples]

Samples

Input #1

3
3 4 6

Output #1

10

$f(11) = (11\ mod\ 3) + (11\ mod\ 4) + (11\ mod\ 6) = 10$ is the maximum value of $f$.

Input #2

5
7 46 11 20 11

Output #2

Input #3

7
994 518 941 851 647 2 581

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Modulo Summation",
    "description": {
      "content": "You are given $N$ positive integers $a_1, a_2, ..., a_N$. For a non-negative integer $m$, let $f(m) = (m\\ mod\\ a_1) + (m\\ mod\\ a_2) + ... + (m\\ mod\\ a_N)$. Here, $X\\ mod\\ Y$ denotes the remainder of t",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc103_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given $N$ positive integers $a_1, a_2, ..., a_N$.\nFor a non-negative integer $m$, let $f(m) = (m\\ mod\\ a_1) + (m\\ mod\\ a_2) + ... + (m\\ mod\\ a_N)$.\nHere, $X\\ mod\\ Y$ denotes the remainder of t...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments