Door Door Door

Time limit1sMemory limit256 MB

Summary

Assign 0 or 1 to each door so no two consecutive doors match and all multiples of 2 agree and all multiples of 3 agree, given door 1.

Level: Medium4 of 10
Topics: Math, Implementation, Number theory, Brute force
Solved: No attempts yet

Problem

Yushin is trapped in a room where he must pass through several doors to get out. Jaehyun, who trapped him, set up a system with unusual rules so that Yushin must open the doors in order, following the rules, and thereby cannot escape.

Rule 1: There are two ways to open a door. You can push it open or pull it open.
Rule 2: You cannot open two consecutive doors the same way.
Rule 3: The doors at multiples of 2 (2nd, 4th, 6th, ...) must all be opened the same way. For example, if the 2nd door is opened by pushing, the 4th door must also be opened by pushing.
Rule 4: The doors at multiples of 3 (3rd, 6th, 9th, ...) must all be opened the same way. For example, if the 3rd door is opened by pushing, the 6th door must also be opened by pushing.

Even though Yushin knows all four rules above, he cannot escape. Write a program that helps Yushin escape the room.

Input

The first line gives the total number of doors $N(2 \le N \le 2{,}500{,}000{,}000)$ .

The second line gives the way Yushin opened the first door. Pushing is written as 0 and pulling is written as 1.

Output

Print the way to open each door from the second door onward, one per line. If escape is impossible, print "Love is open door".

Examples2

Example 1
Input
```
4
0
```
Expected output
```
1
0
1
```
Example 2
Input
```
10
1
```
Expected output
```
Love is open door
```