Date Bugs

Many computers store the year using only a few digits or a fixed-size counter, so after a certain point the displayed year wraps around. A computer that shows only two digits, for example, jumps from 1999 back to 1900. Some systems instead store the number of seconds elapsed since a fixed reference time in a 32-bit integer; after about $2^{32}$ seconds (roughly 136 years) the value wraps back to that reference time.

Each computer $i$ has a bug year $b_i$. While the real year is below $b_i$ the computer shows it correctly, but the moment the real year reaches $b_i$ the display wraps to $a_i$ (instead of $b_i$) and keeps counting up, wrapping again every time it would reach $b_i$. Thus computer $i$ can only ever display a year in the range $[a_i, b_i)$, and when the real year is $Y$ its display is

$\text{display}_i(Y) = a_i + \big((Y - a_i) \bmod (b_i - a_i)\big)$

Several computers each report the year $y_i$ they currently display together with their bug parameters $a_i$ and $b_i$. Assuming every computer refers to the same real year, find the earliest real year consistent with all of them. Because a computer cannot display a year before $a_i$ and cannot predate its own construction, the real year is always at least the maximum of the $a_i$.

The input consists of several test cases. Each test case begins with a line containing an integer $n$ ($1 \le n \le 20$), the number of computers. Each of the next $n$ lines contains three integers $y_i$, $a_i$, $b_i$ ($0 \le a_i \le y_i < b_i < 10000$): $y_i$ is the year the computer displays, $b_i$ is the first year at which the bug occurs (the first year the computer can no longer display), and $a_i$ is the year it wraps to instead.

The input ends with a test case where $n = 0$, which must not be processed.

For the $k$-th test case, first print Case #k:. If a real year consistent with every computer exists, print The actual year is z., where $z$ is the smallest such year that is at least the maximum of the $a_i$. If no such year below 10000 exists, print Unknown bugs detected. instead. Print a blank line between consecutive test cases.