Robot Takahashi

AtCoder

IDabc257_c

Time2000ms

Memory256MB

Difficulty—

There are $N$ people, each of whom is either a child or an adult. The $i$\-th person has a weight of $W_i$. Whether each person is a child or an adult is specified by a string $S$ of length $N$ consisting of `0` and `1`. If the $i$\-th character of $S$ is `0`, then the $i$\-th person is a child; if it is `1`, then the $i$\-th person is an adult. When Takahashi the robot is given a real number $X$, Takahashi judges a person with a weight less than $X$ to be a child and a person with a weight more than or equal to $X$ to be an adult. For a real value $X$, let $f(X)$ be the number of people whom Takahashi correctly judges whether they are children or adults. Find the maximum value of $f(X)$ for all real values of $X$. ## Constraints * $1\leq N\leq 2\times 10^5$ * $S$ is a string of length $N$ consisting of `0` and `1`. * $1\leq W_i\leq 10^9$ * $N$ and $W_i$ are integers. ## Input Input is given from Standard Input in the following format: $N$ $S$ $W_1$ $W_2$ $\ldots$ $W_N$ [samples]

Samples

Input #1

5
10101
60 45 30 40 80

Output #1

4

When Takahashi is given $X=50$, it judges the $2$\-nd, $3$\-rd, and $4$\-th people to be children and the $1$\-st and $5$\-th to be adults.  
In reality, the $2$\-nd and $4$\-th are children, and the $1$\-st, $3$\-rd, and $5$\-th are adults, so the $1$\-st, $2$\-nd, $4$\-th, and $5$\-th people are correctly judged. Thus, $f(50)=4$.
This is the maximum since there is no $X$ that judges correctly for all $5$ people. Thus, $4$ should be printed.

Input #2

3
000
1 2 3

Output #2

3

For example, $X=10$ achieves the maximum value $f(10)=3$.  
Note that the people may be all children or all adults.

Input #3

5
10101
60 50 50 50 60

Output #3

4

For example, $X=55$ achieves the maximum value $f(55)=4$.  
Note that there may be multiple people with the same weight.

API Response (JSON)

{
  "problem": {
    "name": "Robot Takahashi",
    "description": {
      "content": "There are $N$ people, each of whom is either a child or an adult. The $i$\\-th person has a weight of $W_i$.   Whether each person is a child or an adult is specified by a string $S$ of length $N$ cons",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc257_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ people, each of whom is either a child or an adult. The $i$\\-th person has a weight of $W_i$.  \nWhether each person is a child or an adult is specified by a string $S$ of length $N$ cons...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments