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 = [i for i, x in enumerate(input().split()) if int(x) < 0]
a = [-1] + a + [n]

l = [a[i]-a[i-1] for i in range(1, len(a)-1)]
r = [a[i+1]-a[i] for i in range(1, len(a)-1)]

ls = [0 for i in range(len(l))]
if len(ls)>0:
    ls[0] = l[0]
if len(ls)>1:
    ls[1] = l[1]
for i in range(2, len(ls)):
    ls[i] = ls[i-2] + l[i]
    
s_m = 0
for li, ri in zip(ls, r):
##    print(li*ri)
    s_m+=li*ri


s_p = n*(n+1)//2-s_m
print(s_m, s_p)
    
