Erasing Prime Pairs

AtCoder

IDabc263_g

Time2000ms

Memory256MB

Difficulty—

There are integers with $N$ different values written on a blackboard. The $i$\-th value is $A_i$ and is written $B_i$ times. You may repeat the following operation as many times as possible: * Choose two integers $x$ and $y$ written on the blackboard such that $x+y$ is prime. Erase these two integers. Find the maximum number of times the operation can be performed. ## Constraints * $1 \leq N \leq 100$ * $1 \leq A_i \leq 10^7$ * $1 \leq B_i \leq 10^9$ * All $A_i$ are distinct. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $B_1$ $A_2$ $B_2$ $\vdots$ $A_N$ $B_N$ [samples]

Samples

Input #1

Output #1

3

We have $2 + 3 = 5$, and $5$ is prime, so you can choose $2$ and $3$ to erase them, but nothing else. Since there are four $2$s and three $3$s, you can do the operation three times.

Input #2

1
1 4

Output #2

2

We have $1 + 1 = 2$, and $2$ is prime, so you can choose $1$ and $1$ to erase them. Since there are four $1$s, you can do the operation twice.

API Response (JSON)

{
  "problem": {
    "name": "Erasing Prime Pairs",
    "description": {
      "content": "There are integers with $N$ different values written on a blackboard. The $i$\\-th value is $A_i$ and is written $B_i$ times. You may repeat the following operation as many times as possible: *   Choo",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc263_g"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are integers with $N$ different values written on a blackboard. The $i$\\-th value is $A_i$ and is written $B_i$ times.\nYou may repeat the following operation as many times as possible:\n\n*   Choo...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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