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 Python (3.4.3) (judge verdict: Wrong Answer)

N = int(input())
A = []
for i in range(N):
    a = int(input())
    if a>i or (i>0 and a-A[-1]>1):
        print(-1)
        exit()
    A.append(a)

#if A[0]!=0:
#    print(-1)
#    exit()
if sum(A)==0:
    print(0)
    exit()

frag = []
start = 1
next = 2
for i in range(2, N):
    if start!=-1:
        if A[i]==next:#(A[i]==0 or A[i]==1):
            next += 1
        else:
            end = i - 1
            #print(start,end,A[start:end+1])
            frag.append(A[start:end+1])
            if A[i]==0:
                start = -1
            else:
                start = i
                next = A[i] + 1
    elif start==-1 and A[i]!=0:
        if A[i]==1:
            start = i
        else:
            print(-1)
            exit()

#print(start,N-1,A[start:])
frag.append(A[start:])
#print(frag)

ans = 0
for f in frag:
    if f[0]==1:
        ans += len(f)
    else:
        ans += f[0]
print(ans)