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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>
#include<cmath>
using namespace std;

int main() {
    int N;
    cin>>N;
    long A[N];
    for(int i=0;i<N;++i){
        cin>>A[i];
    }
    bool check = true;
    if(A[0]!=0)check = false;
    for(int i=1;i<N;++i){
        if(abs(A[i]-A[i-1])>1)check = false;
    }
    long ans = A[N-1];
    if(check){
        for(int i=N-1;i>=1;--i){
            if(A[i]-A[i-1]!=1)ans += A[i-1];
        }
    }
    else ans = -1;
    cout<<ans<<endl;
}