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 java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.FilterInputStream;
import java.io.BufferedInputStream;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Jenish
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        ScanReader in = new ScanReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        BTheNumberOfProducts solver = new BTheNumberOfProducts();
        solver.solve(1, in, out);
        out.close();
    }

    static class BTheNumberOfProducts {
        public void solve(int testNumber, ScanReader in, PrintWriter out) {
            int n = in.scanInt();
            int arr[] = new int[n];
            in.scanInt(arr);
            long pre[] = new long[n + 1];
            for (int i = 0; i < n; i++) {
                if (arr[i] < 0) pre[i]++;
            }
            for (int i = n - 1; i >= 0; i--) pre[i] = pre[i] + pre[i + 1];
            long odd[] = new long[n + 1];
            long even[] = new long[n + 1];
            for (int i = 0; i < n; i++) {
                if (pre[i] % 2 == 0) {
                    odd[i]++;
                } else {
                    even[i]++;
                }
            }

            for (int i = 1; i < n; i++) {
                odd[i] += odd[i - 1];
                even[i] += even[i - 1];
            }

            long oo = 0;
            long ev = 0;

            for (int i = 0; i < n; i++) {
                if (pre[i + 1] % 2 == 0) {
                    oo += odd[i];
                    ev += even[i];
                } else {
                    oo += even[i];
                    ev += odd[i];
                }
            }

            out.println(ev + " " + oo);
        }

    }

    static class ScanReader {
        private byte[] buf = new byte[4 * 1024];
        private int INDEX;
        private BufferedInputStream in;
        private int TOTAL;

        public ScanReader(InputStream inputStream) {
            in = new BufferedInputStream(inputStream);
        }

        private int scan() {
            if (INDEX >= TOTAL) {
                INDEX = 0;
                try {
                    TOTAL = in.read(buf);
                } catch (Exception e) {
                    e.printStackTrace();
                }
                if (TOTAL <= 0) return -1;
            }
            return buf[INDEX++];
        }

        public int scanInt() {
            int I = 0;
            int n = scan();
            while (isWhiteSpace(n)) n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    I *= 10;
                    I += n - '0';
                    n = scan();
                }
            }
            return neg * I;
        }

        private boolean isWhiteSpace(int n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1) return true;
            else return false;
        }

        public void scanInt(int[] A) {
            for (int i = 0; i < A.length; i++) A[i] = scanInt();
        }

    }
}

