Median Sum

AtCoder

IDagc020_c

Time2000ms

Memory256MB

Difficulty—

You are given $N$ integers $A_1$, $A_2$, ..., $A_N$. Consider the sums of all non-empty subsequences of $A$. There are $2^N - 1$ such sums, an odd number. Let the list of these sums in non-decreasing order be $S_1$, $S_2$, ..., $S_{2^N - 1}$. Find the median of this list, $S_{2^{N-1}}$. ## Constraints * $1 \leq N \leq 2000$ * $1 \leq A_i \leq 2000$ * All input values are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $...$ $A_N$ [samples]

Samples

Input #1

3
1 2 1

Output #1

2

In this case, $S = (1, 1, 2, 2, 3, 3, 4)$. Its median is $S_4 = 2$.

Input #2

1
58

Output #2

58

In this case, $S = (58)$.

API Response (JSON)

{
  "problem": {
    "name": "Median Sum",
    "description": {
      "content": "You are given $N$ integers $A_1$, $A_2$, ..., $A_N$. Consider the sums of all non-empty subsequences of $A$. There are $2^N - 1$ such sums, an odd number. Let the list of these sums in non-decreasing ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc020_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given $N$ integers $A_1$, $A_2$, ..., $A_N$.\nConsider the sums of all non-empty subsequences of $A$. There are $2^N - 1$ such sums, an odd number.\nLet the list of these sums in non-decreasing ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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