Problem:
Score : 700 points

Problem Statement

There is a sequence X of length N, where every element is initially 0. Let X_i denote the i-th element of X.

You are given a sequence A of length N. The i-th element of A is A_i. Determine if we can make X equal to A by repeating the operation below. If we can, find the minimum number of operations required.

Choose an integer i such that 1\leq i\leq N-1. Replace the value of X_{i+1} with the value of X_i plus 1.

Constraints

1 \leq N \leq 2 \times 10^5

0 \leq A_i \leq 10^9(1\leq i\leq N)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

If we can make X equal to A by repeating the operation, print the minimum number of operations required. If we cannot, print -1.

Sample Input 1

4
0
1
1
2

Sample Output 1

3

We can make X equal to A as follows:

Choose i=2. X becomes (0,0,1,0).

Choose i=1. X becomes (0,1,1,0).

Choose i=3. X becomes (0,1,1,2).

Sample Input 2

3
1
2
1

Sample Output 2

-1

Sample Input 3

9
0
1
1
0
1
2
2
1
2

Sample Output 3

8

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using static System.Math;
using static System.Array;
using static AtCoder.Tool;

namespace AtCoder
{
    class AC
    {
        const int mod = 1000000007;
        const int INF = int.MaxValue / 2;
        const long SINF = long.MaxValue / 2;


        static void Main(string[] args)
        {
            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);
            Solve();
            //Console.Out.Flush();
        }
        static void Solve()
        {
            var cin = new Scanner();
            int N = int.Parse(Console.ReadLine());
            long[] A = new long[N];
            for(var i = 0; i < N; i++)
            {
                A[i] = long.Parse(Console.ReadLine());
            }
            long ans = 0;
            if (N == 1)
            {
                Console.WriteLine(A[0] == 0 ? 0 : -1);
            }
            else
            {
                if (A[0] != 0)
                {
                    Console.WriteLine(-1);
                    return;
                }
                for(var i = 1; i < N; i++)
                {
                    if (A[i] == A[i - 1] + 1)
                    {
                        ans++;
                    }
                    else if (A[i] <= A[i - 1])
                    {
                        ans += A[i];
                    }
                    else
                    {
                        ans = -1;
                        break;
                    }
                }
                Console.WriteLine(ans);
            }

        }

    }

    public class Scanner
    {
        public int[] SplitReader()
        {
            int[] array = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return array;
        }
        public long[] SplitReaderL()
        {
            long[] array = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return array;
        }
    }

    public static class Tool
    {
        static public void Initialize<T>(ref T[] array, T initialvalue)
        {
            for(var i = 0; i < array.Length; i++)
            {
                array[i] = initialvalue;
            }
        }
        static public long ModuloP(long value,long mod)
        {
            long r = value % mod;
            
            if (r * mod < 0)
            {
                r += mod;
            }
            return r;
        }

    }

    struct Pair<T> : IComparable<Pair<T>> where T : IComparable<T>
    {
        public T variable;
        public int index;

        public Pair(T val, int i)
        {
            variable = val;
            index = i;
        }

        public int CompareTo(Pair<T> otherPair)
        {
            return variable.CompareTo(otherPair.variable);
        }

        public int CompareIndex(Pair<T> otherPair)
        {
            return index.CompareTo(otherPair.index);
        }
    }


}