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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using System.Runtime.CompilerServices;
using static MyUtil;

class MyUtil
{
    public static int[] ReadIntArray()
    {
	return ReadLine().Split().Select(x => int.Parse(x)).ToArray();
    }
}

class Program
{
    public static void Main()
    {
	var tmp = ReadIntArray();
	int h = tmp[0], w = tmp[1], d = tmp[2];

	var pos = new Tuple<int,int>[h*w+1];
	for (int i = 1; i <= h; i++)
	{
	    var a = ReadIntArray();
	    for (int j = 1; j <= w; j++)
	    {
		pos[a[j-1]] = Tuple.Create(i, j);
	    }
	}

	var s = new int[h*w+1];

	for (int i = d; i <= h*w; i += d)
	{
	    for (int j = 1; j <= d; j++)
	    {
		int n1 = i+j, n0 = n1 - d;
		if (n1 > h*w) break;
		var t0 = pos[n0];
		var t1 = pos[n1];
		int dist = Math.Abs(t1.Item1 - t0.Item1) +
		    Math.Abs(t1.Item2 - t0.Item2);
		s[n1] = s[n0] + dist;
	    }
	}
	
	int q = int.Parse(ReadLine());
	for (int i = 0; i < q; i++)
	{
	    tmp = ReadIntArray();
	    int l = tmp[0], r = tmp[1];
	    WriteLine(s[r] - s[l]);
	}
    }
}