Krypton Stadiums

The planet Krypton has $n$ cities. They sit at distinct points on one straight line running west to east, and they are labelled $0, 1, 2, \dots, n-1$ from west to east. Each city has one team and one stadium.

Stadium $i$ carries two integers $a_i$ and $b_i$. The team from city $x$ plays at stadium $i$ only when $a_i \le x \le b_i$. Every team can play at its home stadium, so $a_i \le i \le b_i$ is guaranteed.

Before the season schedule is written, the layout of the cities and stadiums gets one of three verdicts.

• The layout is Great if for every pair of cities $c_1$ and $c_2$ some stadium $i$ with $\min(c_1, c_2) \le i \le \max(c_1, c_2)$ can host the teams from both cities.
• The layout is Acceptable if it is not Great but for every pair of cities $c_1$ and $c_2$ some stadium can host the teams from both cities.
• The layout is Bad if there is a pair of cities that no stadium can host together.

The input holds several test cases and ends at end of file.

The first line of each test case has the number of cities $n$ ($2 \le n \le 200\,000$). The next $n$ lines give the intervals of stadiums $0$ through $n-1$ in order. Each line has exactly six characters: the first three give $a_i$ and the last three give $b_i$. Each group of three characters is a three digit base 62 number that uses 0-9A-Za-z as the digits with values $0$ through $61$. For example, cities $0$, $1$, $9$, $10$, $35$, $36$, $61$, $62$ and $199\,999$ are written 000, 001, 009, 00A, 00Z, 00a, 00z, 010 and q1n. Always $0 \le a_i \le i \le b_i \le n-1$.

There are at most $1\,000$ test cases and at most $2\,000\,000$ stadiums over all test cases.

For each test case print one of Great, Acceptable or Bad on its own line.