Maya Calendar

Interview

Time limit1sMemory limit128 MB

Summary

Convert n dates from the Haab calendar to the Tzolkin calendar using modular arithmetic on the day index.

Level: Medium4 of 10
Topics: Math, Implementation, Simulation, Number theory
Solved: No attempts yet

Problem

Professor M. A. Ya has been studying the ancient Maya calendars and needs a program to convert dates from one of them to the other.

The Haab calendar has a 365-day year divided into 19 months. Each of the first 18 months has 20 days, and the days are numbered from 0 to 19. The names of these 18 months, in order, are:

pop, no, zip, zotz, tzec, xul, yoxkin, mol, chen, yax, zac, ceh, mac, kankin, muan, pax, koyab, cumhu

The 19th and last month is called uayet and has only 5 days, numbered 0 to 4, so a year has $18 \times 20 + 5 = 365$ days. The Maya considered this month unlucky.

The Tzolkin calendar (the holy year) has a 260-day year. Each day is described by a pair: a number together with a day name. There are 20 day names, used in a cycle:

imix, ik, akbal, kan, chicchan, cimi, manik, lamat, muluk, ok, chuen, eb, ben, ix, mem, cib, caban, eznab, canac, ahau

together with the 13 numbers $1$ through $13$ , also used in a cycle. The number and the name advance together by one each day, so every day has an unambiguous description. For example, the first days of a Tzolkin year are:

1 imix, 2 ik, 3 akbal, 4 kan, 5 chicchan, 6 cimi, 7 manik, 8 lamat, 9 muluk, 10 ok, 11 chuen, 12 eb, 13 ben, 1 ix, 2 mem, 3 cib, 4 caban, 5 eznab, 6 canac, 7 ahau, 8 imix, 9 ik, 10 akbal, ...

Years in both calendars are numbered $0, 1, 2, \ldots$ , where year $0$ marks the beginning of the world. The very first day is therefore:

Haab: 0. pop 0
Tzolkin: 1 imix 0

Given dates in the Haab calendar, convert each one to the corresponding Tzolkin date.

Input

Each Haab date is written in the format:

NumberOfTheDay. Month Year

The first line of input contains the number of dates $n$ . Each of the next $n$ lines contains one date in Haab format. Every year is smaller than $5000$ .

Output

For each input date, output the corresponding Tzolkin date in the format:

Number NameOfTheDay Year

The first line of output is the number of dates $n$ . The next $n$ lines contain the converted Tzolkin dates, in the same order as the input.

Examples2

Example 1

Input

3
10. zac 0
0. pop 0
10. zac 1995

Expected output

3
3 chuen 0
1 imix 0
9 cimi 2801

Example 2
Input
```
1
0. pop 0
```
Expected output
```
1
1 imix 0
```