Pepe the frog needs to jump across a river while only stepping on some stones! He needs to jump from column to column (left to right in the input). Rock means the rock on row . However, jumping from row to takes time.

#### Input

The first line of the input contains two integers, and , the number of columns and the number of positions of rocks.

Each subsequent lines of the input contains of a string of `0`

s and `1`

s. A `1`

on line (starting from 2nd line) on column (both 0-indexed) indicates the rock is present in column , a `0`

indicates that rock is not present.

#### Output

Output the minimum amount of time taken to jump to the end.

You are guaranteed there is at least one possible way to jump to the end.

#### Constraints

Subtask 1 (10%)

Subtask 2 (5%)

Subtask 3 (20%)

Subtask 4 (20%)

Subtask 5 (45%)

#### Sample Input 1

```
5 3
11100
00011
11111
```

#### Sample Output 1

`0`

#### Sample Input 1 Explanation

You don't need to jump, just use rock 3 throughout.

#### Sample Input 2

```
5 5
10000
01000
00100
00010
00001
```

#### Sample Output 2

`4`

#### Sample Input 2 Explanation

Start from rock 0, change to rock 1, change to rock 2, etc. Each of them takes 1 time because they are adjacent.

## Comments

in sample case 2 pepe must jump diagonally. how many columns can he jump, and how does that affect the time taken?

He can only move one column and one column only, meaning he can't even go down in the row on the same column.

TLEMy solution has an execution time of O(NClogC), which should be fast enough. However, I am TLEing. Is there maybe a reason for this occurring? Thank you!

Edit: I changed a couple parts to reduce the execution time and it worked, but it is still really weird why my initial O(NClogC) TLEd. Some suggestions on why my initial solution TLEd would be much appreciated. Thanks!

With a sub 1 second time limit on the problem, it's a possibility that you got a slow judge on some submissions and a fast judge on other submissions. Normally that wouldn't be the difference between an AC and TLE, the tight time limit probably caused that, even though there was nothing wrong with your code.

Ah yes, very true. But it is still weird, since NClogC is on the order of magnitude of 40 million operations. I am not too sure about this, but can't a computer do about 1 billion operations in a second? Thank you!

Sorry, just to clarify, does the frog have to visit every column or is the frog technically allowed to jump from a rock in column 1 directly to a rock in column N?

e.g.

Is the answer 2 or 0?

Thanks!

The input

3 2

101

010

Gave me 2, so I think the frog does need to visit each column.

Edit: format

Awesome, thank you for the confirmation!

The time constraint for this question is quite strict. It is not guaranteed to be solvable by languages other than

`C++`

. Even then you will need quite a bit of constant optimization to pass (assuming you have the optimal time complexity).Can frog jump back or just forward? And can frog move between different stones within the same column?

Is answer for this test is 2?

Based on my submission, the frog can only jump forward. The case you provided is the same as

and the answer is 2.

The frog cannot jump between different rows in the same column. Agree with ZQFMGB12. 18 is the best answer for your case.