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: Time Limit Exceeded)

n = gets.chomp.to_i
ary = []
n.times do |i|
  tmp = gets.chomp.to_i
  ary << tmp
end

# -1の処理
flag = true
flag = false if ary[0]!=0
(ary.length-1).times do |i|
  if ary[i+1]-ary[i]>1
    flag = false
  end
end

if flag
  count = 0
  ary.reverse!
  tmp_ary = Array.new(ary.length, 0)

  ary.length.times do |i|
    if ary[i]!=tmp_ary[i]
      count+=ary[i]
      ary[i].times do |j|
        tmp_ary[i+j]=ary[i]-j
      end
    end
  end

  puts(count)
else
  puts(-1)
end