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 Scala (2.11.7) (judge verdict: Wrong Answer)

import java.util.Scanner

import scala.collection.mutable.ArrayBuffer

object Main {
  def main(args: Array[String]): Unit = println(solve(new Scanner(System.in)))

  def solve(in: String): String = solve(new Scanner(in))

  def solve(sc: Scanner): String = {
    val N = sc.nextInt
    val A = Array.fill(N)(sc.nextInt)
    val B = ArrayBuffer.fill(N)(0)

    var ans = 0
    for (i <- (N - 1) to 0 by -1) {
      if (A(i) > i) {
        return "-1"
      }
      for (j <- 0 until A(i)) {
        val n = A(i) - j
        if (B(i - j) < n) {
          B(i - j) = n
          ans += 1
        } else if (B(i - j) > n) {
          return "-1"
        }

      }
      println(B)
    }
    ans.toString
  }
}