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 Go (1.6) (judge verdict: Accepted)

package main

import (
  "fmt"
)

func main() {
  var N int
  fmt.Scan(&N)
  var A int
  s := 0
  cnt := -1
  for i := 0; i < N; i++ {
    fmt.Scan(&A)
    if A > i + 1 {
      cnt = -1
      break
    }
    if i - A < s {
      cnt = -1
      break
    }
    if i - A == s {
      cnt += 1
    } else {
      cnt += A
      s = i - A
    }
  }
  fmt.Println(cnt)
}