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 (3.8.2) (judge verdict: Wrong Answer)

N=int(input())

A0=int(input())
if A0!=0:
    print(-1)
    exit()

ans=0
temp=0
f=0
for i in range(N-1):
    A=int(input())
    if A-A0>1:
        print(-1)
        exit()
    if A == 0:
        if f==0:
            temp=temp-A0+1
        ans += temp
        temp = 0
        f=0
    elif A==A0:
        temp+=A
        f+=1
    elif A<A0:
        temp=temp-A0+1
        temp+=A
        f=0
    else:
        temp+=A
        f=0

    A0=A

ans+=temp
if f==0:
    ans=ans-A0+1

print(ans)