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 C {
	int MAX = 10000;
	double EPS = 1e-12;
	
	void run() {
		int n = in.nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = in.nextInt();
		}
		double low = - MAX;
		double high = MAX;
		double ans = 0;
		while (low + EPS < high) {
			double x = (low + high) / 2;
			double maxSum = 0, minSum = 0;
			double minPref = 0, maxPref = 0, pref = 0;
			for (int i = 0; i < n; i++) {
				pref += a[i] - x;
				maxSum = Math.max(maxSum, pref - minPref);
				minSum = Math.min(minSum, pref - maxPref);
				maxPref = Math.max(maxPref, pref);
				minPref = Math.min(minPref, pref);
			}
			ans = (maxSum - minSum) * 0.5;
			if (maxSum > -minSum) {
				low = x;
			} else {
				high = x;
			}
		}
		System.out.println(ans);
	}

	static MyScanner in;
	static PrintWriter out;

	public static void main(String[] args) throws IOException {
		boolean stdStreams = true;
		String fileName = C.class.getSimpleName().replaceFirst("_.*", "").toLowerCase();
		String inputFileName = fileName + ".in";
		String outputFileName = fileName + ".out";
		
		Locale.setDefault(Locale.US);
		BufferedReader br;
		if (stdStreams) {
			br = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
		} else {
			br = new BufferedReader(new FileReader(inputFileName));
			out = new PrintWriter(outputFileName);
		}
		in = new MyScanner(br);
		int tests = 1;//in.nextInt();
		for (int test = 0; test < tests; test++) {
			new C().run();
		}
		br.close();
		out.close();
	}
	
	static class MyScanner {
		BufferedReader br;
		StringTokenizer st;

		MyScanner(BufferedReader br) {
			this.br = br;
		}
		
		void findToken() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
		}
		
		String next() {
			findToken();
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		
		long nextLong() {
			return Long.parseLong(next());
		}
		
		double nextDouble() {
			return Double.parseDouble(next());
		}
	}
}