Problem C
Checkout

Single 1, triple 5, bullseye, for a total of $1+3\cdot 5+50= 66$. Photo: Jeremy Bishop

You recently started playing darts and want to learn the “$501$” variant.

Players take turns throwing three darts; the aim is to reduce your score from $501$ to $0$. The darts board contains of slices numbered $1$ to $20$, with the obvious scoring rule: when your dart hits $17$ (called “single $17$” in darts lingo), your score is reduced by $17$. Each of the twenty slices contains smaller areas called “double” and “triple”; hitting “double $6$” reduces your score by $2\cdot 6 = 12$, hitting ”triple $4$” reduces it by $3\cdot 4 = 12$”. In the middle of the darts board, ”single bull” is worth $25$ points, “bullseye” is worth $50$.

In the $501$ variant, your final throw—called the checkout—must reduce your score to $0$ using a double or bullseye. (Not a triple, and not single bull.)

It is difficult to calculate the scores in the heat of the game—instead you write a problem to help you.

Input

The only line of input contains an integer $2 \leq T \leq 501$, your current score.

Output

If it is not possible to reduce your score to $0$ with at most three throws, print “impossible”. Otherwise, output between one and three lines. Each line contains a dart throw, either of the form “single bull” or “bullseye”, or of the form “single $s$”, “double $s$”, or “triple $s$”, for integer $s\in \{ 1,\ldots , 20\} $. The total points of all throws must equal $T$ and the last throw must be either “bullseye” or a “double”. If there are multiple valid answers, output any of them.

42

triple 13
single 1
double 1

90

triple 13
single 1
bullseye

270

impossible