The Number of Products
Description
You are given a sequence $a_1, a_2, \dots, a_n$ consisting of $n$ non-zero integers (i.e. $a_i \ne 0$).
You have to calculate two following values:
- the number of pairs of indices $(l, r)$ $(l \le r)$ such that $a_l \cdot a_{l + 1} \dots a_{r - 1} \cdot a_r$ is negative;
- the number of pairs of indices $(l, r)$ $(l \le r)$ such that $a_l \cdot a_{l + 1} \dots a_{r - 1} \cdot a_r$ is positive;
The first line contains one integer $n$ $(1 \le n \le 2 \cdot 10^{5})$ — the number of elements in the sequence.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ $(-10^{9} \le a_i \le 10^{9}; a_i \neq 0)$ — the elements of the sequence.
Print two integers — the number of subsegments with negative product and the number of subsegments with positive product, respectively.
Input
The first line contains one integer $n$ $(1 \le n \le 2 \cdot 10^{5})$ — the number of elements in the sequence.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ $(-10^{9} \le a_i \le 10^{9}; a_i \neq 0)$ — the elements of the sequence.
Output
Print two integers — the number of subsegments with negative product and the number of subsegments with positive product, respectively.
Samples
5
5 -3 3 -1 1
8 7
10
4 2 -4 3 1 2 -4 3 2 3
28 27
5
-1 -2 -3 -4 -5
9 6