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: Wrong Answer)

n = gets.to_i
a = n.times.map{gets.to_i}
ans = Array.new(n,0)
(n-1).downto(1) do |i|
  if a[i] == a[i-1]+1
    ans[i] += 1
  elsif a[i] <= a[i-1] && a[i] != 0
    ans[i] += 1
    if a[i] != 1
      ans[i-1] += 1
    end
  elsif a[i] != 0
    puts "-1"
    exit
  end
end
if a[0] == 0
  puts ans.inject(:+)
else
  puts "-1"
end