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 Ruby (2.3.3) (judge verdict: Accepted)

N = gets.to_i
as = N.times.map{gets.to_i}
if as[0] != 0
    puts -1
    exit
end

last = as[-1] == 0 ? nil : as[-1]
now = as[-1]
ans = 0
(N-2).downto(0).each do |i|
    unless last
        if as[i] == 0
            next
        else
            last = as[i]
            now = as[i]
            next
        end
    end
    if as[i] == now - 1
        if as[i] == 0
            ans += last
            last = nil
        else
            now = as[i]
        end
    elsif as[i] < now - 1
        puts -1
        exit
    else
        ans += last
        last = as[i]
        now = as[i]
    end
end

puts ans