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
n = int(input())
a = list(map(int, input().split()))

dp1 = [0] * n
dp2 = [0] * n

if 0 < a[0]: dp1[0] = 1
if 0 > a[0]: dp2[0] = 1

for i in range(1, n):
    if 0 < a[i]:
        dp1[i] = dp1[i-1] + 1
        dp2[i] = dp2[i-1]

    if 0 > a[i]:
        dp1[i] = dp2[i-1]
        dp2[i] = dp1[i-1] + 1

pos = sum(dp1)
neg = sum(dp2)

print(neg, pos)