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
def solve(n,ar):
    ans_p =0
    ans_n = 0
    pos = 0
    neg = 0

    for i in range(n):
        if ar[i] > 0: ans_p += 1
        else: ans_n += 1

    if ar[0] > 0:
        flag = True
    else:
        flag = False

    for i in range(1,n):
        if flag is True:
            if ar[i] > 0: pos += 1
            else:
                neg += 1
                flag = False
        else:
            if ar[i] > 0: neg += 1
            else:
                pos += 1
                flag = True

    dp = [[0]*2 for _ in range(n)]
    dp[0][0] = neg
    dp[0][1] = pos
    neg,pos = 0,0

    for i in range(1,n):
        if ar[i-1] > 0 and ar[i] < 0:
            dp[i][0] = max(0,dp[i-1][0] -1)
            dp[i][1] = dp[i-1][1]

        elif ar[i-1] < 0 and ar[i] > 0:
            dp[i][0] = dp[i-1][1]
            dp[i][1] = max(dp[i-1][0]-1,0)

        elif ar[i-1] < 0 and ar[i] < 0:
            dp[i][0] = max(0,dp[i-1][1]-1)
            dp[i][1] = dp[i-1][0]
        else:
            dp[i][0] = dp[i-1][0]
            dp[i][1] = max(dp[i-1][1]-1,0)

    for i in range(n):
        neg += dp[i][0]
        pos += dp[i][1]

    ans_n += neg
    ans_p += pos

    print(ans_n, ans_p)
    return









if __name__ == '__main__':
    n = int(input())
    ar = list(map(int,input().split()))

    solve(n,ar)