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B. The Number of Products

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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;

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.

Examples

Input

5 5 -3 3 -1 1

Output

8 7

Input

10 4 2 -4 3 1 2 -4 3 2 3

Output

28 27

Input

5 -1 -2 -3 -4 -5

Output

9 6

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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