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
a = []
n.times{a << gets.to_i}
a.reverse!
i = 0
ctn = 0
if a[-1] != 0
    puts "-1"
    exit
end
while i < a.length - 1
    if a[i] != 0
        ar = []
        while a[i] >= a[i+1]
            if a[i] - a[i+1] > 1
                puts "-1"
                exit
            end
            ar << a[i]
            i += 1
            break if i == a.length - 1
        end
        ar << a[i]
        prev = ar[0]
        ctn += prev
        ar.shift
        while ar != []
            if ar.first == prev
                ctn += ar.first
            end
            prev = ar.first
            ar.shift
        end
    end
    i += 1
end
puts ctn