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 OCaml (4.10.0) (judge verdict: Wrong Answer)

Scanf.scanf "%d" (fun n ->
    let a = Array.init n (fun _ -> Scanf.scanf " %d" (fun a -> a)) in
    let rec loop i expect acc =
        if i = 0 then (if expect = 0 then acc else -1) else
            if a.(i) < expect then -1 else
                loop (i - 1) (max 0 (a.(i) - 1)) (if expect = a.(i) then acc else acc + a.(i))
    in
    loop (n - 1) 0 0 |> Printf.printf "%d\n"
)