F. Football
time limit per test
3 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

Scientists are researching an impact of football match results on the mood of football fans. They have a hypothesis that there is a correlation between the number of draws and fans' desire to watch football matches in the future.

In football, two teams play a match. The teams score goals throughout a match. A score "$x$:$y$" means that the team we observe scored $x$ goals and conceded $y$ goals. If $x = y$, then the match ends in a draw. If $x > y$, then the observed team wins, and if $x < y$, then it loses.

To find out if there is a correlation, the scientists gathered information about the results of teams in lower leagues. The information they found is the number of matches played by the team ($n$), the number of goals scored in these matches ($a$), and the number of goals conceded in these matches ($b$).

You are given this information for a single team. You are asked to calculate the minimum number of draws that could have happened during the team's matches and provide a list of match scores with the minimum number of draws.

Input

The first line contains an integer $n$ — the number of matches played by the team ($1 \le n \le 100$). The second line contains an integer $a$ — the total number of goals scored by the team in all $n$ matches ($0 \le a \le 1000$). The third line contains an integer $b$ — the total number of goals conceded by the team in all $n$ matches ($0 \le b \le 1000$).

Output

In the first line, print a single integer $d$ — the minimum number of draws.

In the following $n$ lines, print a list of match scores, each line in the format "$x$:$y$", where $x$ is the number of goals scored in the match, and $y$ – the number of goals conceded, so that exactly $d$ of these matches have ended in a draw. In case multiple such lists of match scores exist, print any of them.

Examples
Input
3
2
4
Output
0
1:0
1:2
0:2
Input
1
2
2
Output
1
2:2
Input
4
0
7
Output
0
0:1
0:2
0:1
0:3
Input
6
3
1
Output
2
0:0
1:0
0:0
0:1
1:0
1:0