F - Eating Symbols Hard

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

はじめ，高橋君が思い浮かべている整数列 A のすべての要素は 0 です． また，整数 P の値は 0 です．

• + を食べた場合，A_P の値が 1 大きくなる．
• - を食べた場合，A_P の値が 1 小さくなる．
• > を食べた場合，P の値が 1 大きくなる．
• < を食べた場合，P の値が 1 小さくなる．

### 制約

• 1 \leq N \leq 250000
• |S| = N
• S の各文字は +, -, >, < のいずれか

### 入力

N
S


### 入力例 1

5
+>+<-


### 出力例 1

3


• (1, 5)
• (2, 3)
• (2, 4)

### 入力例 2

5
+>+-<


### 出力例 2

5


### 入力例 3

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


### 出力例 3

475


Score : 1200 points

### Problem Statement

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


### Sample Input 1

5
+>+<-


### Sample 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)

### Sample Input 2

5
+>+-<


### Sample Output 2

5


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

### Sample Input 3

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


### Sample Output 3

475