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 }
if a[0] != 0
  puts -1
  exit
end
(n - 1).times do |i|
  if a[i + 1] - a[i] >= 2
    puts -1
    exit
  end
end
ans = 0

s = []
prev = -1
cnt = 1
a.each do |ai|
  if prev == ai
    cnt += 1
  else
    s << [prev, cnt]
    cnt = 1
    prev = ai
  end
  ans += 1 if ai != 0
end
s << [prev, cnt]
s.shift
# p s
s.each do |ai, m|
  next if ai == 0 || ai == 1
  ans += (2 ** (ai - 2)) * (m - 1)
end
p ans