You are given a sequence a_1, a_2, ..., a_n consisting of n non-zero integers (i.e. a_i ≠ 0). 

You have to calculate two following values:

  1. the number of pairs of indices (l, r) (l ≤ r) such that a_l ⋅ a_{l + 1} ... a_{r - 1} ⋅ a_r is negative; 
  2. the number of pairs of indices (l, r) (l ≤ r) such that a_l ⋅ a_{l + 1} ... a_{r - 1} ⋅ a_r is positive; 

Input

The first line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^{5}) — the number of elements in the sequence.

The second line contains n integers a_1, a_2, ..., a_n (-10^{9} ≤ a_i ≤ 10^{9}; a_i ≠ 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
import sys
input = sys.stdin.readline

n = int(input())
a = list(map(int, input().split()))
ans_pos, ans_neg = 0, 0
prev_pos, prev_neg = 0, 0

for ai in a:
    if ai > 0:
        next_pos = prev_pos+1
        next_neg = prev_neg
    elif ai < 0:
        next_pos = prev_neg
        next_neg = prev_pos+1
        
    ans_pos += next_pos
    ans_neg += next_neg
    
    prev_pos, prev_neg = next_pos, next_neg
    
print(ans_neg, ans_pos)