Powers of two

AtCoder

IDagc029_b

Time2000ms

Memory256MB

Difficulty—

Takahashi has $N$ balls with positive integers written on them. The integer written on the $i$\-th ball is $A_i$. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of $2$. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed. Here, a positive integer is said to be a power of $2$ when it can be written as $2^t$ using some non-negative integer $t$. ## Constraints * $1 \leq N \leq 2\times 10^5$ * $1 \leq A_i \leq 10^9$ * $A_i$ is an integer. ## 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 3

Output #1

1

We can form one pair whose sum of the written numbers is $4$ by pairing the first and third balls. Note that we cannot pair the second ball with itself.

Input #2

5
3 11 14 5 13

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Powers of two",
    "description": {
      "content": "Takahashi has $N$ balls with positive integers written on them. The integer written on the $i$\\-th ball is $A_i$. He would like to form some number of pairs such that the sum of the integers written o",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc029_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi has $N$ balls with positive integers written on them. The integer written on the $i$\\-th ball is $A_i$. He would like to form some number of pairs such that the sum of the integers written o...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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