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 rep(i,x,y) for (int i=(x);i<=(y);i++)
#define ll long long
#define inf 1000000001
using namespace std;
ll read(){
	char ch=getchar();ll x=0;int op=1;
	for (;!isdigit(ch);ch=getchar()) if (ch=='-') op=-1;
	for (;isdigit(ch);ch=getchar()) x=(x<<1)+(x<<3)+ch-'0';
	return x*op;
}
#define N 200005
int n,a[N],tong[N];ll ans;
void failed(){puts("-1");exit(0);}
int main(){
	n=read();
	rep (i,1,n) a[i]=read();
	if (a[1]!=0) failed();
	rep (i,2,n) if (a[i]-a[i-1]>1) failed();
	for (int i=1;i<=n;){
		int st=i,ed=i;
		while (ed<n&&a[ed+1]>=a[ed]) ed++;
		rep (j,st,ed) tong[a[j]]++;
		rep (j,a[st],a[ed]){
//			cerr<<"j="<<j<<": "<<tong[j]<<'\n';
			ans+=(ll)j*(tong[j]-1);
		}
		ans+=a[ed];
//		if (a[st]>1) ans+=a[st];
		rep (j,st,ed) tong[a[j]]--;
		i=ed+1;
	}
	cout<<ans<<'\n';
	return 0;
}