2017-like Number

AtCoder

IDabc084_d

Time2000ms

Memory256MB

Difficulty—

We say that a odd number $N$ is _similar to 2017_ when both $N$ and $(N+1)/2$ are prime. You are given $Q$ queries. In the $i$\-th query, given two odd numbers $l_i$ and $r_i$, find the number of odd numbers $x$ similar to 2017 such that $l_i ≤ x ≤ r_i$. ## Constraints * $1≤Q≤10^5$ * $1≤l_i≤r_i≤10^5$ * $l_i$ and $r_i$ are odd. * All input values are integers. ## Input Input is given from Standard Input in the following format: $Q$ $l_1$ $r_1$ $:$ $l_Q$ $r_Q$ [samples]

Samples

Input #1

1
3 7

Output #1

2

*   $3$ is similar to 2017, since both $3$ and $(3+1)/2=2$ are prime.
*   $5$ is similar to 2017, since both $5$ and $(5+1)/2=3$ are prime.
*   $7$ is not similar to 2017, since $(7+1)/2=4$ is not prime, although $7$ is prime.

Thus, the response to the first query should be $2$.

Input #2

Output #2

1
0
0
1

Note that $2017$ is also similar to 2017.

Input #3

Output #3

API Response (JSON)

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  "problem": {
    "name": "2017-like Number",
    "description": {
      "content": "We say that a odd number $N$ is _similar to 2017_ when both $N$ and $(N+1)/2$ are prime. You are given $Q$ queries. In the $i$\\-th query, given two odd numbers $l_i$ and $r_i$, find the number of odd ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc084_d"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We say that a odd number $N$ is _similar to 2017_ when both $N$ and $(N+1)/2$ are prime.\nYou are given $Q$ queries.\nIn the $i$\\-th query, given two odd numbers $l_i$ and $r_i$, find the number of odd ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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