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)

//https://atcoder.jp/contests/agc024/tasks/agc024_c
//C - Sequence Growing Easy
#include <bits/stdc++.h>
#if LOCAL
#include "dump.hpp"
#else
#define dump(...)
#endif
using namespace std;
using ll=long long;
#define FOR(i,a,b) for(ll i=(a);i<(b);++i)
#define REP(i,n) FOR(i,0,n)
template<class T>bool chmax(T &a, const T &b) {if (a<b) { a=b; return 1; } return 0;}
template<class T>bool chmin(T &a, const T &b) {if (b<a) { a=b; return 1; } return 0;}
int main() {
    ll N; cin>>N;
    vector<ll> an(N);
    for(auto&&a:an){
        cin>>a;
    }
    bool ans_flag=(an.at(0)==0);
    ll count=0;
    //貪欲,x(i)=x(i+1)+1 だと +1
    //x(i)<=x(i+1) だと +x(i+1)
    for(ll i=1;i<an.size();++i){
        if(an.at(i)>an.at(i-1)+1){
            ans_flag=false;
        }else if(an.at(i)==an.at(i-1)+1){
            count += 1;
        }else{
            count += an.at(i);
        }
    }
    if(not ans_flag) count=-1;
    cout<<count<<endl;
    return 0;
}