One day, Twilight Sparkle is interested in how to sort a sequence of integers a1, a2, ..., an in non-decreasing order. Being a young unicorn, the only operation she can perform is a unit shift. That is, she can move the last element of the sequence to its beginning:

a1, a2, ..., an → an, a1, a2, ..., an - 1.

Help Twilight Sparkle to calculate: what is the minimum number of operations that she needs to sort the sequence?

Input

The first line contains an integer n (2 ≤ n ≤ 105). The second line contains n integer numbers a1, a2, ..., an (1 ≤ ai ≤ 105).

Output

If it's impossible to sort the sequence output -1. Otherwise output the minimum number of operations Twilight Sparkle needs to sort it.

Examples

Input

2
2 1


Output

1


Input

3
1 3 2


Output

-1


Input

2
1 2


Output

0
//package codeforcespracice;

import java.io.*;
import java.util.*;
public class littlepony  {
    public static void main(String[] args) throws Exception
    {
        InputReader in=new InputReader(System.in);
        PrintWriter pw=new PrintWriter(System.out);
        int n=in.nextInt();
        int[] arr=new int[n];
        for(int i=0;i<n;i++)
        {
            arr[i]=in.nextInt();
        }
        boolean decreasing=false;
        int count=0;
        int last=-1;
        for(int i=1;i<n;i++)
        {
            if(arr[i]<arr[i-1] && !decreasing)
            {
                decreasing=true;
                count++;
            }
            else
            {
                if(arr[i]<arr[i-1])
                {
                    System.out.println(-1);
                    System.exit(0);
                }
                if(decreasing)
                {
                count++;
                }
            }
            
        }
        if(decreasing && arr[n-1]>arr[0])
        {
            System.out.println(-1);
            System.exit(0);
        }
        pw.println(count);
        
        pw.close();
    }
    static class pair
    {
        int x,y,maping;
        pair(int x,int y)
        {
            this.x=x;
            this.y=y;
        }
        
    }
    
    
    
    
    
    
    
     static class InputReader {

        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar;
        private int snumChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int snext() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }

            int res = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));

            return res * sgn;
        }
        
        public long nextLong() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }

            long res = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));

            return res * sgn;
        }
        
        public String readString() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

}
