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.*;
import java.awt.Point;
import java.math.BigDecimal;
import java.math.BigInteger;

import static java.lang.Math.*;


public class C implements Runnable{
	
	// SOLUTION!!! 
	// HACK ME PLEASE IF YOU CAN!!!
	// PLEASE!!!
	// PLEASE!!!
	// PLEASE!!!
	
	protected static final int ITERATIONS = 100;
	void solve() throws IOException {
		int n = readInt();
		int[] a = readIntArray(n);
		
		double left = -10000, right = 10000;
		for (int iteration = 0; iteration < ITERATIONS; ++iteration) {
			double mLeft = left + (right - left) / 3;
			double mRight = right - (right - left) / 3;
			
			double fLeft = f(n, a, mLeft);
			double fRight = f(n, a, mRight);
			
			if (fLeft < fRight) {
				right = mRight;
			} else {
				left = mLeft;
			}
		}
		
		double ansX = (left + right) / 2;
		double ansWeakness = f(n, a, ansX);
		
		out.println(ansWeakness);
	}
	
	double f(int n, int[] a, double x) {
		double maxWeakness = 0;
		
		double minPrefixSum = 0, maxPrefixSum = 0;
		
		double prefixSum = 0;
		for (int value : a) {
			prefixSum += value - x;
			
			minPrefixSum = min(minPrefixSum, prefixSum);
			maxPrefixSum = max(maxPrefixSum, prefixSum);
			
			maxWeakness = max(maxWeakness, abs(prefixSum - minPrefixSum));
			maxWeakness = max(maxWeakness, abs(maxPrefixSum - prefixSum));
		}
		
		return maxWeakness;
	}
	
	/////////////////////////////////////////////////////////////////////
	
	final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
	
	BufferedReader in;
	OutputWriter out;
	StringTokenizer tok = new StringTokenizer("");
	
	public static void main(String[] args){
		new Thread(null, new C(), "", 128 * (1L << 20)).start();
	}
	
	/////////////////////////////////////////////////////////////////////
	
	void init() throws FileNotFoundException{
		Locale.setDefault(Locale.US);
		
		if (ONLINE_JUDGE){
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new OutputWriter(System.out);
		}else{
			in = new BufferedReader(new FileReader("input.txt"));
			out = new OutputWriter("output.txt");
		}
	}
	
	////////////////////////////////////////////////////////////////
	
	long timeBegin, timeEnd;

	void time(){
		timeEnd = System.currentTimeMillis();
		System.err.println("Time = " + (timeEnd - timeBegin));
	}
	
	void debug(Object... objects){
		if (ONLINE_JUDGE){
			for (Object o: objects){
				System.err.println(o.toString());
			}
		}
	}
	
	/////////////////////////////////////////////////////////////////////
	
	public void run(){
		try{
			timeBegin = System.currentTimeMillis();
			Locale.setDefault(Locale.US);
			
			init();
			solve();
			
			out.close();
			time();
		}catch (Exception e){
			e.printStackTrace(System.err);
			System.exit(-1);
		}
	}
	
	/////////////////////////////////////////////////////////////////////
	
	String delim = " ";
	
	String readString() throws IOException{
		while(!tok.hasMoreTokens()){
			try{
				tok = new StringTokenizer(in.readLine());
			}catch (Exception e){
				return null;
			}
		}
		
		return tok.nextToken(delim);
	}
	
	String readLine() throws IOException{
		return in.readLine();
	}
	
	/////////////////////////////////////////////////////////////////
	
	final char NOT_A_SYMBOL = '\0';
	
	char readChar() throws IOException{
		int intValue = in.read();
		
		if (intValue == -1){
			return NOT_A_SYMBOL;
		}
		
		return (char) intValue;
	}
	
	char[] readCharArray() throws IOException{
		return readLine().toCharArray();
	}
	
	/////////////////////////////////////////////////////////////////
	
	int readInt() throws IOException {
		return Integer.parseInt(readString());
	}
	
	int[] readIntArray(int size) throws IOException {
		int[] array = new int[size];
		
		for (int index = 0; index < size; ++index){
			array[index] = readInt();
		}
		
		return array;
	}
	
	int[] readSortedIntArray(int size) throws IOException {
		Integer[] array = new Integer[size];
		
		for (int index = 0; index < size; ++index) {
			array[index] = readInt();
		}
		Arrays.sort(array);
		
		int[] sortedArray = new int[size];
		for (int index = 0; index < size; ++index) {
			sortedArray[index] = array[index];
		}
		
		return sortedArray;
	}
	
	int[] readIntArrayWithDecrease(int size) throws IOException {
		int[] array = readIntArray(size);
		
		for (int i = 0; i < size; ++i) {
			array[i]--;
		}
		
		return array;
	}
	
	///////////////////////////////////////////////////////////////////
	
	int[][] readIntMatrix(int rowsCount, int columnsCount) throws IOException {
		int[][] matrix = new int[rowsCount][];
		
		for (int rowIndex = 0; rowIndex < rowsCount; ++rowIndex) {
			matrix[rowIndex] = readIntArray(columnsCount);
		}
		
		return matrix;
	}
	
	int[][] readIntMatrixWithDecrease(int rowsCount, int columnsCount) throws IOException {
		int[][] matrix = new int[rowsCount][];
		
		for (int rowIndex = 0; rowIndex < rowsCount; ++rowIndex) {
			matrix[rowIndex] = readIntArrayWithDecrease(columnsCount);
		}
		
		return matrix;
	}
	
	///////////////////////////////////////////////////////////////////
	
	long readLong() throws IOException{
		return Long.parseLong(readString());
	}
	
	long[] readLongArray(int size) throws IOException{
		long[] array = new long[size];
		
		for (int index = 0; index < size; ++index){
			array[index] = readLong();
		}
		
		return array;
	}
	
	////////////////////////////////////////////////////////////////////
	
	double readDouble() throws IOException{
		return Double.parseDouble(readString());
	}
	
	double[] readDoubleArray(int size) throws IOException{
		double[] array = new double[size];
		
		for (int index = 0; index < size; ++index){
			array[index] = readDouble();
		}
		
		return array;
	}
	
	////////////////////////////////////////////////////////////////////
		
	BigInteger readBigInteger() throws IOException {
		return new BigInteger(readString());
	}
	
	BigDecimal readBigDecimal() throws IOException {
		return new BigDecimal(readString());
	}
	
	/////////////////////////////////////////////////////////////////////
	
	Point readPoint() throws IOException{
		int x = readInt();
		int y = readInt();
		return new Point(x, y);
	}
	
	Point[] readPointArray(int size) throws IOException{
		Point[] array = new Point[size];
		
		for (int index = 0; index < size; ++index){
			array[index] = readPoint();
		}
		
		return array;
	}
	
	/////////////////////////////////////////////////////////////////////
	
	List<Integer>[] readGraph(int vertexNumber, int edgeNumber)
	throws IOException{
		@SuppressWarnings("unchecked")
		List<Integer>[] graph = new List[vertexNumber];
		
		for (int index = 0; index < vertexNumber; ++index){
			graph[index] = new ArrayList<Integer>();
		}
		
		while (edgeNumber-- > 0){
			int from = readInt() - 1;
			int to = readInt() - 1;
			
			graph[from].add(to);
			graph[to].add(from);
		}
		
		return graph;
	}
	
	/////////////////////////////////////////////////////////////////////
	
	static class IntIndexPair {
		
		static Comparator<IntIndexPair> increaseComparator = new Comparator<IntIndexPair>() {
			
			@Override
			public int compare(IntIndexPair indexPair1, IntIndexPair indexPair2) {
				int value1 = indexPair1.value;
				int value2 = indexPair2.value;
				
				if (value1 != value2) return value1 - value2;
				
				int index1 = indexPair1.index;
				int index2 = indexPair2.index;
				
				return index1 - index2;
			}
		};
		
		static Comparator<IntIndexPair> decreaseComparator = new Comparator<IntIndexPair>() {
			
			@Override
			public int compare(IntIndexPair indexPair1, IntIndexPair indexPair2) {
				int value1 = indexPair1.value;
				int value2 = indexPair2.value;
				
				if (value1 != value2) return -(value1 - value2);
				
				int index1 = indexPair1.index;
				int index2 = indexPair2.index;
				
				return index1 - index2;
			}
		};
		
		int value, index;

		public IntIndexPair(int value, int index) {
			super();
			this.value = value;
			this.index = index;
		}		
		
		public int getRealIndex() {
			return index + 1;
		}
	}
	
	IntIndexPair[] readIntIndexArray(int size) throws IOException {
		IntIndexPair[] array = new IntIndexPair[size];
		
		for (int index = 0; index < size; ++index) {
			array[index] = new IntIndexPair(readInt(), index);
		}
		
		return array;
	}
	
	/////////////////////////////////////////////////////////////////////
	
	static class OutputWriter extends PrintWriter {

		final int DEFAULT_PRECISION = 12;
		
		protected int precision;
		protected String format, formatWithSpace;
		
		{
			precision = DEFAULT_PRECISION;
			
			format = createFormat(precision);
			formatWithSpace = format + " ";
		}
		
		public OutputWriter(OutputStream out) {
			super(out);
		}

		public OutputWriter(String fileName) throws FileNotFoundException {
			super(fileName);
		}
		
		public int getPrecision() {
			return precision;
		}

		public void setPrecision(int precision) {
			precision = max(0, precision);
			this.precision = precision;
			
			format = createFormat(precision);
			formatWithSpace = format + " ";
		}
		
		private String createFormat(int precision){
			return "%." + precision + "f";
		}
		
		@Override
		public void print(double d){
			printf(format, d);
		}
		
		public void printWithSpace(double d){
			printf(formatWithSpace, d);
		}

		public void printAll(double...d){
			for (int i = 0; i < d.length - 1; ++i){
				printWithSpace(d[i]);
			}
			
			print(d[d.length - 1]);
		}
		
		@Override
		public void println(double d){
			printlnAll(d);
		}
		
		public void printlnAll(double... d){
			printAll(d);
			println();
		}
	}
	
	/////////////////////////////////////////////////////////////////////
	
	static final int[][] steps = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}}; 
	static final int[][] steps8 = {
			{-1, 0}, {1, 0}, {0, -1}, {0, 1},
			{-1, -1}, {1, 1}, {1, -1}, {-1, 1}
	};
	
	static final boolean check(int index, int lim){
		return (0 <= index && index < lim);
	}
	
	/////////////////////////////////////////////////////////////////////
	
	static final boolean checkBit(int mask, int bit){
		return (mask & (1 << bit)) != 0;
	}
	
	/////////////////////////////////////////////////////////////////////
	
	static final long getSum(int[] array) {
		long sum = 0;
		for (int value: array) {
			sum += value;
		}
		
		return sum;
	}
	
	static final Point getMinMax(int[] array) {
		int min = array[0];
		int max = array[0];
		
		for (int index = 0, size = array.length; index < size; ++index, ++index) {
			int value = array[index];
			
			if (index == size - 1) {
				min = min(min, value);
				max = max(max, value);
			} else {
				int otherValue = array[index + 1];
				
				if (value <= otherValue) {
					min = min(min, value);
					max = max(max, otherValue);
				} else {
					min = min(min, otherValue);
					max = max(max, value);
				}
			}
		}
		
		return new Point(min, max);
	}
}