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
//package test;

import java.util.Scanner;

public class starter {

	public static void main(String[] args)
		throws Exception 
	{
			Scanner conio = new Scanner ( System.in ) ;
	
			int n = conio.nextInt() ;
			
			long holder[] = new long  [n] ;
			
			for ( int i = 0 ; i < n ; ++i )
				holder[i] = conio.nextInt() ;
			
			long cnt1 = 0 ;
			long cnt2 = 0 ; 
			long bal = 0 , result = 0 ;
			
			for ( int i = 0 ; i < n ; ++i )
			{
				if ( bal % 2 == 0  )
					++cnt1 ;
				else
					++cnt2 ;
				
				if ( holder[i] < 0 )
				{
					++bal ;
				}
				
				if ( bal % 2 == 0 )
					result += cnt1 ;
				else
					result += cnt2 ; 
					

			}
			
			long total = n*((long)n+1) / 2 ;
			
			
			System.out.println( (total - result) + " " + result ) ; 
			
			
			conio.close() ;
			
	}

}
