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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.security.KeyPair;
import java.util.*;

public class Main {

    static long[][] c ;
    static long[] arr;
    static long n , m , k;
    static long dp[][][];
    static int[] parent; /// DSU

    public static void main(String[] args) throws IOException {
        Reader.init(System.in);
        int n = Reader.nextInt();
        long[] arr = new long[n];
        int p = 1;
        int cnt = 0;
        long[] pos = new long[n+1];
        long[] neg = new long[n+1];
        long cnt1 = 0;
        long cnt2 =0;
        for (int i = 0 ; i < n ; i++){
            long t = Reader.nextLong();
            if (t>0){
                p*=1;
            }
            else {
                p*=-1;
            }
            arr[i] = p;

            if (i==0){
                if (arr[i]>0){
                    cnt1++;
                }
                else{
                    cnt2++;
                }
            }
            else {
                if (arr[i]>0){
                    cnt1++;
                }
                else{
                    cnt2++;
                }

                if (arr[i]>0){
                    cnt1+=pos[i-1];
                    cnt2+=neg[i-1];
                }
                else{
                    cnt1+=neg[i-1];
                    cnt2+=pos[i-1];
                }
            }

            if (i==0){
                if (arr[i]>0){
                    pos[i]++;
                }
                else{
                    neg[i]++;
                }
            }
            else{
                if (arr[i]>0){
                    pos[i] = pos[i-1]+1;
                    neg[i] = neg[i-1];
                }
                else{
                    neg[i] = neg[i-1] +1;
                    pos[i] = pos[i-1];
                }

            }

            //System.out.println(cnt2 + " " + cnt1);

        }

        //System.out.println(Arrays.toString(pos));
        //System.out.println(Arrays.toString(neg));

        System.out.println(cnt2 + " " + cnt1);









    }

    static int find(int a){
        if (parent[a]!=a){
            parent[a] = find(parent[a]);
        }
        return parent[a];
    }



    public static void sortbyColumn_asc(int arr[][], int col)
    {
        // Using built-in sort function Arrays.sort
        Arrays.sort(arr, new Comparator<int[]>() {

            @Override
            // Compare values according to columns
            public int compare(final int[] entry1,
                               final int[] entry2) {

                // To sort in descending order revert
                // the '>' Operator
                if (entry1[col] > entry2[col])
                    return 1;
                else
                    return -1;
            }
        });  // End of function call sort().
    }

    public static void sortbyColumn_dsc(int arr[][], int col)
    {
        // Using built-in sort function Arrays.sort
        Arrays.sort(arr, new Comparator<int[]>() {

            @Override
            // Compare values according to columns
            public int compare(final int[] entry1,
                               final int[] entry2) {

                // To sort in descending order revert
                // the '>' Operator
                if (entry1[col] > entry2[col])
                    return -1;
                else
                    return 1;
            }
        });  // End of function call sort().
    }

    static void swap(char[] arr , int i , int j){
        char tmp = arr[i];
        arr[i] = arr[j];
        arr[j] = tmp;
    }

    static void swap(int[] arr , int i , int j){
        int tmp = arr[i];
        arr[i] = arr[j];
        arr[j] = tmp;
    }





}

class Node implements Comparable<Node>{
    int a ;
    int b;
    Node(int a , int b){
        this.a = a;
        this.b = b;
    }
    public int compareTo(Node o) {
        return -1*(this.a - o.a);
    }
}
class Edge implements Comparable<Edge>{
    int x , y , w;

    public Edge(int x, int y, int w) {
        this.x = x;
        this.y = y;
        this.w = w;
    }

    @Override
    public int compareTo(Edge o) {
        return this.w - o.w;
    }
}
class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
        reader = new BufferedReader(
                new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }
    /** get next word */
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                    reader.readLine() );
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
    static long nextLong() throws IOException {
        return Long.parseLong( next() );
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
}
class MergeSort
{
    // Merges two subarrays of arr[].
    // First subarray is arr[l..m]
    // Second subarray is arr[m+1..r]
    void merge(int arr[], int l, int m, int r)
    {
        // Find sizes of two subarrays to be merged
        int n1 = m - l + 1;
        int n2 = r - m;

        /* Create temp arrays */
        int L[] = new int [n1];
        int R[] = new int [n2];

        /*Copy data to temp arrays*/
        for (int i=0; i<n1; ++i)
            L[i] = arr[l + i];
        for (int j=0; j<n2; ++j)
            R[j] = arr[m + 1+ j];


        /* Merge the temp arrays */

        // Initial indexes of first and second subarrays
        int i = 0, j = 0;

        // Initial index of merged subarry array
        int k = l;
        while (i < n1 && j < n2)
        {
            if (L[i] <= R[j])
            {
                arr[k] = L[i];
                i++;
            }
            else
            {
                arr[k] = R[j];
                j++;
            }
            k++;
        }

        /* Copy remaining elements of L[] if any */
        while (i < n1)
        {
            arr[k] = L[i];
            i++;
            k++;
        }

        /* Copy remaining elements of R[] if any */
        while (j < n2)
        {
            arr[k] = R[j];
            j++;
            k++;
        }
    }

    // Main function that sorts arr[l..r] using
    // merge()
    void sort(int arr[], int l, int r)
    {
        if (l < r)
        {
            // Find the middle point
            int m = (l+r)/2;

            // Sort first and second halves
            sort(arr, l, m);
            sort(arr , m+1, r);

            // Merge the sorted halves
            merge(arr, l, m, r);
        }
    }

    /* A utility function to print array of size n */
    static void printArray(int arr[])
    {
        int n = arr.length;
        for (int i=0; i<n; ++i)
            System.out.print(arr[i] + " ");
        System.out.println();
    }

    // Driver method

}