# Calculating Dart Scores

*double*area and a

*triple*area. When the dart hits the

*double*area of section $i$ the player scores $2 i$ points, and when the dart hits the

*triple*area the player scores $3 i$ points, instead of $i$ points. When throwing three darts, the player can therefore score a total of at most $180$ points by throwing all three darts in the triple area of section $20$.

Given a target score, output at most three throw scores such that their sum is equal to the given target score. Note that the centre of the dartboard, which is usually called bullseye, is not taken into account is this problem.

## Input

The input consists of a single integer $n$ ($1\leq n \leq 180$), the target score.

## Output

If the target score can be achieved, output at most three
lines, each of the form “`single
$d$`”, “`double $d$`”, or “`triple $d$`”, where $d$ is an integer between $1$ and $20$ (inclusive), such that the sum of
these scores is equal to $n$. Otherwise, output “`impossible`”. If there are multiple valid
answers you may output any of them.

Sample Input 1 | Sample Output 1 |
---|---|

180 |
triple 20 triple 20 triple 20 |

Sample Input 2 | Sample Output 2 |
---|---|

96 |
triple 19 double 15 single 9 |

Sample Input 3 | Sample Output 3 |
---|---|

27 |
triple 9 |