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 <.

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