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 PHP (7.4.4) (judge verdict: Wrong Answer)

<?php
list($n) = ints();
for ($i = 0; $i < $n; ++$i) list($a[]) = ints();
if ($n === 1 && $a[0] === 0) exit('0');
if ($a[0] !== 0) exit('-1');
$ans = 0;
for ($i = $n - 1; $i >= 1; --$i) {
    if ($a[$i] > $a[$i] + 1) exit('-1');
    if ($a[$i] === 0) continue;
    ++$ans;
    if ($a[$i] > 1 && $a[$i - 1] >= $a[$i]) $ans += $a[$i] - 1;
}
echo $ans;
function ints()
{
    return array_map('intval', explode(' ', trim(fgets(STDIN))));
}