Two Airlines

AtCoder

IDarc177_f

Time5000ms

Memory256MB

Difficulty—

The Republic of AtCoder consists of $L+1$ islands aligned east-west, numbered $0$ to $L$ from west to east. The islands are connected by air routes, where for each $1 \leq i \leq L$, there is a bidirectional air route between islands $i-1$ and $i$, as shown in the figure below. Each air route is owned by company A or company J, and the route between islands $i-1$ and $i$ is owned by company $S_i$. ![image](https://img.atcoder.jp/arc177/dacd06e6239af911b67dfbb502b35bcd.png) The nation has $N$ residents, numbered $1$ to $N$. Resident $i$ is currently on island $X_i$. Each resident has a **coupon** of one of the companies. Specifically, resident $i$ has a coupon of company $C_i$. With a coupon, a resident can take that company's routes for free **any number of times**, but taking a route of the other company costs $1$ coin per trip. Now, there is a treasure chest on island $0$. The residents want to cooperate to carry it to the capital, which is on island $L$. Determine the minimum total number of coins required to achieve this goal. The residents can pass the treasure chest to each other, but not their coupons. ## Constraints * $1 \leq L \leq 6 \times 10^4$ * $1 \leq N \leq 6 \times 10^4$ * $S_i \ (1 \leq i \leq L)$ is `A` or `J`. * $0 \leq X_i \leq L \ (1 \leq i \leq N)$ * $C_i \ (1 \leq i \leq N)$ is `A` or `J`. * $L$, $N$, and $X_i$ are integers. ## Input The input is given from Standard Input in the following format: $L$ $N$ $S_1$$S_2$$\cdots$$S_L$ $X_1$ $C_1$ $X_2$ $C_2$ $\vdots$ $X_N$ $C_N$ Note that the second line is given as a string of length $L$. [samples]

Samples

Input #1

4 3
AAJJ
3 A
1 J
1 J

Output #1

2

The following procedure carries the treasure chest to island $4$ for a total of $2$ coins.

1.  Resident $1$ moves from island $3$ to island $2$. The route is not covered by the coupon, so $1$ coin is paid.
2.  Resident $1$ moves from island $2$ to island $1$. The route is covered by the coupon, so no coin is needed.
3.  Resident $1$ moves from island $1$ to island $0$. The route is covered by the coupon, so no coin is needed.
4.  Resident $1$ picks up the treasure chest.
5.  Resident $1$, carrying the treasure chest, moves from island $0$ to island $1$. The route is covered by the coupon, so no coin is needed.
6.  Resident $1$ passes the treasure chest to resident $2$.
7.  Resident $2$, carrying the treasure chest, moves from island $1$ to island $2$. The route is not covered by the coupon, so $1$ coin is paid.
8.  Resident $2$, carrying the treasure chest, moves from island $2$ to island $3$. The route is covered by the coupon, so no coin is needed.
9.  Resident $2$, carrying the treasure chest, moves from island $3$ to island $4$. The route is covered by the coupon, so no coin is needed.

![image](https://img.atcoder.jp/arc177/9545d9fbdd7defc8d56f84380765a3d7.png)

Input #2

8 3
JJAAJJAJ
2 A
6 A
8 J

Output #2

Input #3

8 6
JJAAJJAJ
2 A
6 A
8 J
8 J
8 J
8 J

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Two Airlines",
    "description": {
      "content": "The Republic of AtCoder consists of $L+1$ islands aligned east-west, numbered $0$ to $L$ from west to east. The islands are connected by air routes, where for each $1 \\leq i \\leq L$, there is a bidire",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 5000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc177_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "The Republic of AtCoder consists of $L+1$ islands aligned east-west, numbered $0$ to $L$ from west to east. The islands are connected by air routes, where for each $1 \\leq i \\leq L$, there is a bidire...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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