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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;
import java.awt.*;

public class Main {
  public static void main(String args[]) {
    Scanner sc = new Scanner(System.in);

    int N = sc.nextInt();
    int[] A = new int[N];
    for (int i = 0; i < N; i++) {
      A[i] = sc.nextInt();
    }

    long ans = 0;
    int prev_a = -1;

    for (int i = N-1; i >= 0; i--) {
      if (A[i] >= prev_a - 1 && A[i] <= i) {
        if (A[i] > prev_a - 1) {
          ans += A[i];
        }
        prev_a = A[i];
      } else {
        ans = -1;
        break;
      }
    }

    System.out.println(ans);
  }
}