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.InputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Comparator;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.Map;
import java.util.PriorityQueue;
import java.math.BigDecimal;
import java.math.BigInteger;
    
public class Main{

static final InputStream in=System.in;
static final PrintWriter out=new PrintWriter(System.out);
static final int INF=Integer.MAX_VALUE;
static final long LINF=Long.MAX_VALUE/2;
static int n;
static int[] a;

public static void main(String[] args) throws IOException{
InputReader ir=new InputReader(in);
n=ir.nextInt();
a=ir.nextIntArray(n);
double lb=-10000;
double ub=10000;
for(int i=0;i<100;i++){
  double lmid=(lb+lb+ub)/3;
  double umid=(lb+ub+ub)/3;
  if(f(umid)>=f(lmid)) ub=umid;
  else lb=lmid;
}
out.printf("%.15f\n",f((lb+ub)/2));
out.flush();
}

public static double f(double x){
  double res=0;
  double sum; int p;
  sum=0;
  p=0;
  while(true){
    while(p<n){
      sum+=a[p++]-x;
      res=Math.max(res,sum);
      if(sum<0){
        sum=0;
        break;
      }
    }
    if(p==n) break;
  }
  sum=0;
  p=0;
  while(true){
    while(p<n){
      sum+=x-a[p++];
      res=Math.max(res,sum);
      if(sum<0){
        sum=0;
        break;
      }
    }
    if(p==n) break;
  }
  return res;
}

static class InputReader {
private InputStream in;
private byte[] buffer=new byte[1024];
private int curbuf;
private int lenbuf;

public InputReader(InputStream in) {this.in=in;}
  
public int readByte() {
if(lenbuf==-1) throw new InputMismatchException();
if(curbuf>=lenbuf){
curbuf= 0;
try{
lenbuf=in.read(buffer);
}
catch (IOException e) {
throw new InputMismatchException();
}
if(lenbuf<=0)
return -1;
}
return buffer[curbuf++];
}

public boolean isSpaceChar(int c){return !(c>=33&&c<=126);}

private int skip() {int b; while((b = readByte())!=-1&&isSpaceChar(b)); return b;}

public String next() {
int b=skip();
StringBuilder sb=new StringBuilder();
while(!isSpaceChar(b)){
sb.appendCodePoint(b);
b=readByte();
}
return sb.toString();
}
 
public int nextInt() {
int c=readByte();
while (isSpaceChar(c)) c=readByte();
boolean minus=false;
if (c=='-') {
minus=true;
c=readByte();
}
int res=0;
do{
if(c<'0'||c>'9') throw new InputMismatchException();
res=res*10+c-'0';
c=readByte();
}while(!isSpaceChar(c));
return (minus)?-res:res;
}

public long nextLong() {
int c=readByte();
while (isSpaceChar(c)) c=readByte();
boolean minus=false;
if (c=='-') {
minus=true;
c=readByte();
}
long res = 0;
do{
if(c<'0'||c>'9') throw new InputMismatchException();
res=res*10+c-'0';
c=readByte();
}while(!isSpaceChar(c));
return (minus)?-res:res;
}

public double nextDouble(){return Double.parseDouble(next());}

public BigInteger nextBigInteger(){return new BigInteger(next());}

public int[] nextIntArray(int n){
int[] a=new int[n];
for(int i=0;i<n;i++) a[i]=nextInt();
return a;
}
}
}