Three Colors

AtCoder

IDtenka1_2019_d

Time3000ms

Memory256MB

Difficulty—

You are given $N$ integers. The $i$\-th integer is $a_i$. Find the number, modulo $998244353$, of ways to paint each of the integers red, green or blue so that the following condition is satisfied: * Let $R$, $G$ and $B$ be the sums of the integers painted red, green and blue, respectively. There exists a triangle with positive area whose sides have lengths $R$, $G$ and $B$. ## Constraints * $3 \leq N \leq 300$ * $1 \leq a_i \leq 300(1\leq i\leq N)$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $a_1$ $:$ $a_N$ [samples]

Samples

Input #1

Output #1

18

We can only paint the integers so that the lengths of the sides of the triangle will be $1$, $2$ and $2$, and there are $18$ such ways.

Input #2

Output #2

Input #3

Output #3

563038556

API Response (JSON)

{
  "problem": {
    "name": "Three Colors",
    "description": {
      "content": "You are given $N$ integers. The $i$\\-th integer is $a_i$. Find the number, modulo $998244353$, of ways to paint each of the integers red, green or blue so that the following condition is satisfied: *",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "tenka1_2019_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given $N$ integers. The $i$\\-th integer is $a_i$. Find the number, modulo $998244353$, of ways to paint each of the integers red, green or blue so that the following condition is satisfied:\n\n*...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments