Problem: You are given a sequence of n integers a1, a2, ..., an. 

Determine a real number x such that the weakness of the sequence a1 - x, a2 - x, ..., an - x is as small as possible.

The weakness of a sequence is defined as the maximum value of the poorness over all segments (contiguous subsequences) of a sequence.

The poorness of a segment is defined as the absolute value of sum of the elements of segment.

Input

The first line contains one integer n (1 ≤ n ≤ 200 000), the length of a sequence.

The second line contains n integers a1, a2, ..., an (|ai| ≤ 10 000).

Output

Output a real number denoting the minimum possible weakness of a1 - x, a2 - x, ..., an - x. Your answer will be considered correct if its relative or absolute error doesn't exceed 10 - 6.

Examples

Input

3
1 2 3


Output

1.000000000000000


Input

4
1 2 3 4


Output

2.000000000000000


Input

10
1 10 2 9 3 8 4 7 5 6


Output

4.500000000000000

Note

For the first case, the optimal value of x is 2 so the sequence becomes  - 1, 0, 1 and the max poorness occurs at the segment "-1" or segment "1". The poorness value (answer) equals to 1 in this case. 

For the second sample the optimal value of x is 2.5 so the sequence becomes  - 1.5, - 0.5, 0.5, 1.5 and the max poorness occurs on segment "-1.5 -0.5" or "0.5 1.5". The poorness value (answer) equals to 2 in this case.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
public class WeaknessAndPoorness
{
	public static void main(String[] args) throws Exception
	{
		FastScanner in = new FastScanner(System.in);
		
		int n = in.nextInt();
		
		int[] array = new int[n];
		for(int x = 0; x < n; x++)
		{
			array[x] = in.nextInt();
		}
		
		double low = -10000;
		double high = 10000;
		for(int i = 0; i < 100; i++)
		{
			double mid1 = (low + low + high) / 3;
			double mid2 = (low + high + high) / 3;
			
			if(calc(array, mid1) < calc(array, mid2))
			{
				high = mid2;
			}
			else
			{
				low = mid1;
			}
		}
		
		System.out.println(calc(array, low));
	}
	
	public static double calc(int[] array, double mid)
	{
		return Math.max(poorness(array, mid, 1), poorness(array, mid, -1));
	}
	
	public static double poorness(int[] array, double x, double s)
	{
		double ret = 0;
		double current = 0;
		for(int i = 0; i < array.length; i++)
		{
			current = Math.max(0, current + s * (array[i] - x));
			ret = Math.max(ret, current);
		}
		
		return ret;
	}
	
	static class FastScanner
	{
		BufferedReader br;
		StringTokenizer st;
		
		public FastScanner(InputStream input)
		{
			br = new BufferedReader(new InputStreamReader(input));
			st = new StringTokenizer("");
		}
		
		public String next() throws IOException
		{
			if(st.hasMoreTokens())
			{
				return st.nextToken();
			}
			else
			{
				st = new StringTokenizer(br.readLine());
				return next();
			}
		}
		
		public int nextInt() throws IOException
		{
			return Integer.parseInt(next());
		}
	}
}