Eating Symbols Hard

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

Output

Print the answer.

Examples

Input

5 +>+<-

Output

3

Input

5 +>+-<

Output

5

Input

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

Output

475

inputFormat

Input

Input is given from Standard Input in the following format:

N S

outputFormat

Output

Print the answer.

Examples

Input

5 +>+<-

Output

3

Input

5 +>+-<

Output

5

Input

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

Output

475

样例

5
+>+<-

3