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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

# coding: utf-8
# Your code here!
n=int(input())
a=[]
for i in range(n):
    a.append(int(input()))
#a=a[::-1]
ans=0
pos=n
pre=0
b=a[0]
for i in range(n):
    x=a.pop()
    if x==0:
        continue
    elif x>pos-1:
        ans=-1
        break
    else:
        if x==pre-1:
            pre=x
            continue
        else:
            if x>=pre:
                pre=x
                ans+=x
            else:
                ans=-1
                break
    pos-=1
if b>0:
    ans=-1
print(ans)