Eating Symbols Hard

AtCoder

IDarc099_d

Time2000ms

Memory256MB

Difficulty—

In Takahashi's mind, there is always an integer sequence of length $2 \times 10^9 + 1$: $A = (A_{-10^9}, A_{-10^9 + 1}, ..., A_{10^9 - 1}, A_{10^9})$ and an integer $P$. Initially, all the elements in the sequence $A$ in Takahashi's mind are $0$, and the value of the integer $P$ is $0$. When Takahashi eats symbols `+`, `-`, `>` and `<`, the sequence $A$ and the integer $P$ will change as follows: * When he eats `+`, the value of $A_P$ increases by $1$; * When he eats `-`, the value of $A_P$ decreases by $1$; * When he eats `>`, the value of $P$ increases by $1$; * When he eats `<`, the value of $P$ decreases by $1$. Takahashi has a string $S$ of length $N$. Each character in $S$ is one of the symbols `+`, `-`, `>` and `<`. He chose a pair of integers $(i, j)$ such that $1 \leq i \leq j \leq N$ and ate the symbols that are the $i$\-th, $(i+1)$\-th, $...$, $j$\-th characters in $S$, in this order. We heard that, after he finished eating, the sequence $A$ became the same as if he had eaten all the symbols in $S$ from first to last. How many such possible pairs $(i, j)$ are there? ## Constraints * $1 \leq N \leq 250000$ * $|S| = N$ * Each character in $S$ is `+`, `-`, `>` or `<`. ## Input Input is given from Standard Input in the following format: $N$ $S$ [samples]

Samples

Input #1

5
+>+<-

Output #1

3

If Takahashi eats all the symbols in $S$, $A_1 = 1$ and all other elements would be $0$. The pairs $(i, j)$ that leads to the same sequence $A$ are as follows:

*   $(1, 5)$
*   $(2, 3)$
*   $(2, 4)$

Input #2

5
+>+-<

Output #2

5

Note that the value of $P$ may be different from the value when Takahashi eats all the symbols in $S$.

Input #3

48
-+><<><><><>>>+-<<>->>><<><<-+<>><+<<>+><-+->><<

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Eating Symbols Hard",
    "description": {
      "content": "In Takahashi's mind, there is always an integer sequence of length $2 \\times 10^9 + 1$: $A = (A_{-10^9}, A_{-10^9 + 1}, ..., A_{10^9 - 1}, A_{10^9})$ and an integer $P$. Initially, all the elements in",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc099_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "In Takahashi's mind, there is always an integer sequence of length $2 \\times 10^9 + 1$: $A = (A_{-10^9}, A_{-10^9 + 1}, ..., A_{10^9 - 1}, A_{10^9})$ and an integer $P$.\nInitially, all the elements in...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments