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: Accepted)

#include <bits/stdc++.h>
#define FOR(i, begin, end) for(int i=(begin);i<(end);i++)
#define REP(i, n) FOR(i,0,n)
#define IFOR(i, begin, end) for(int i=(end)-1;i>=(begin);i--)
#define IREP(i, n) IFOR(i,0,n)
#define SORT(a) sort(a.begin(), a.end())
#define REVERSE(a) reverse(a.begin(), a.end())
#define int long long
#define INF 1000000000000000
using namespace std;

typedef vector<int> vec;
typedef vector<vec> mat;
typedef pair<int, int> Pii;

template<typename T>
void readvec(vector<T> &a);
void readindex(vector<int> &a);



signed main(){

    int N; cin >> N;
    vec A(N); readvec(A);

    int ans = 0;

    int z = N;
    N--;
    while(N >= 0){
        if(A[N] > N || N - A[N] > z){
            cout << -1;
            return 0;
        }
        z = N - A[N];
        int n = N, a = A[N];
        ans += a;
        REP(i, n + 1){
            if(A[n - i] != a - i) break;
            N--;
        }
    }

    cout << ans;
    
    return 0;
}


template<typename T>
void readvec(vector<T> &a){
    REP(i, a.size()){
        cin >> a[i];
    }
}
void readindex(vector<int> &a){
    REP(i, a.size()){
        cin >> a[i];
        a[i]--;
    }
}