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.io.*;
import java.util.*;


public class Code {

	public static void main (String[] args) {
        MyScanner scanner = new MyScanner();
        
        final int N = scanner.nextInt();
        final int[] array = new int[N];
        
        for (int i=0; i<N; i++) {
            array[i] = scanner.nextInt();
        }
        
        double left = -10_000;
        double right = 10_000;
        
        // while (Math.abs(right - left) >= 1e-12) {
        for (int i = 0; i < 100; i++) {
            double mid1 = left + (right - left) / 3;
            double mid2 = right - (right - left) / 3;
            // System.out.printf("%f %f %f %f\n", left, mid1, mid2, right);
            double f1 = weakness(array, mid1);
            double f2 = weakness(array, mid2);
            if (f1 < f2) {
                right = mid2;
            } else {
                left = mid1;
            }
        }

        System.out.printf("%.10f", weakness(array, left));
	}
    
    private static double weakness(int[] array, double x) {
        double maxSum = 0;
        double sum = 0;
        for (int i=0; i<array.length; i++) {
            sum += array[i] - x;
            maxSum = Math.max(maxSum, sum);
            if (sum < 0) {
                sum = 0;
            }
        }
        
        sum = 0;
        for (int i=0; i<array.length; i++) {
            sum += array[i] - x;
            maxSum = Math.max(maxSum, -sum);
            if (sum > 0) {
                sum = 0;
            }
        }
        
        return maxSum;
    }
    
    public static class MyScanner {
      BufferedReader br;
      StringTokenizer st;
 
      public MyScanner() {
         br = new BufferedReader(new InputStreamReader(System.in));
      }
 
      String next() {
          while (st == null || !st.hasMoreElements()) {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          }
          return st.nextToken();
      }
 
      int nextInt() {
          return Integer.parseInt(next());
      }
 
      long nextLong() {
          return Long.parseLong(next());
      }
 
      double nextDouble() {
          return Double.parseDouble(next());
      }
 
      String nextLine(){
          String str = "";
	  try {
	     str = br.readLine();
	  } catch (IOException e) {
	     e.printStackTrace();
	  }
	  return str;
      }

   }
}