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 Python (3.4.3) (judge verdict: Accepted)

# 最初は0から始まる
# その次は、今の数+1以下である必要がある。
# 今の数+2以上が現れたらNG
# 通常は（0以外のときに）ans += 1
# 同じ数以下のとき、たとえば5 -> 3となっているときは、
# それまでに3を作れているはずなので、3を足す

N = int(input())
cur = 0
ans = 0
for i in range(N):
  a = int(input())
  if i == 0 and a != 0:
    print(-1)
    exit(0)
  elif a == 0:
    ans += 0
  elif a == cur + 1:
    ans += 1
  elif a <= cur:
    ans += a
  else:
    print(-1)
    exit(0)
  cur = a
print(ans)