Equal Cut

AtCoder

IDarc100_b

Time2000ms

Memory256MB

Difficulty—

Snuke has an integer sequence $A$ of length $N$. He will make three cuts in $A$ and divide it into four (non-empty) contiguous subsequences $B, C, D$ and $E$. The positions of the cuts can be freely chosen. Let $P,Q,R,S$ be the sums of the elements in $B,C,D,E$, respectively. Snuke is happier when the absolute difference of the maximum and the minimum among $P,Q,R,S$ is smaller. Find the minimum possible absolute difference of the maximum and the minimum among $P,Q,R,S$. ## Constraints * $4 \leq N \leq 2 \times 10^5$ * $1 \leq A_i \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $...$ $A_N$ [samples]

Samples

Input #1

5
3 2 4 1 2

Output #1

2

If we divide $A$ as $B,C,D,E=(3),(2),(4),(1,2)$, then $P=3,Q=2,R=4,S=1+2=3$. Here, the maximum and the minimum among $P,Q,R,S$ are $4$ and $2$, with the absolute difference of $2$. We cannot make the absolute difference of the maximum and the minimum less than $2$, so the answer is $2$.

Input #2

10
10 71 84 33 6 47 23 25 52 64

Output #2

Input #3

7
1 2 3 1000000000 4 5 6

Output #3

999999994

API Response (JSON)

{
  "problem": {
    "name": "Equal Cut",
    "description": {
      "content": "Snuke has an integer sequence $A$ of length $N$. He will make three cuts in $A$ and divide it into four (non-empty) contiguous subsequences $B, C, D$ and $E$. The positions of the cuts can be freely c",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc100_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Snuke has an integer sequence $A$ of length $N$.\nHe will make three cuts in $A$ and divide it into four (non-empty) contiguous subsequences $B, C, D$ and $E$. The positions of the cuts can be freely c...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments