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: Accepted)

import sys
def input(): return sys.stdin.readline().rstrip()
def main():
    n=int(input())
    A=[int(input())for _ in range(n)]
    if A[0]!=0:
        print(-1)
        sys.exit()
    dp=[0]*n
    for i,a in enumerate(A[1:],1):
        if a>=A[i-1]+2:
            print(-1) 
            sys.exit()
        elif a==A[i-1]+1:
            dp[i]=1
        else:
            dp[i]=a
    print(sum(dp))

if __name__=='__main__':
    main()