A spacecraft's life-support computer keeps a log of cabin temperature readings. Each log entry records a unique entry id, the mission day it was taken on, and the temperature reading (an integer, which may be negative). Entries are not necessarily stored in chronological order.

An entry is a warming entry if the log also contains a reading for the mission day immediately before it (mission day minus one) and this entry's temperature is strictly greater than that previous day's temperature. Find every warming entry.

Input format

• Line 1: a single integer N — the number of log entries.
• Next N lines: each containing three space-separated integers id, day, and temp — the entry's id, mission day, and temperature reading.

Output format

• Line 1: an integer K — the number of warming entries.
• Next K lines: the id of each warming entry, one per line, ordered by increasing mission day.

Constraints

• 1 <= N <= 1000
• All id values are distinct, and all day values are distinct.
• 1 <= id, day <= 10^6
• -100 <= temp <= 100

4
1 1 10
2 2 25
3 3 20
4 4 30

2
2
4

3
11 8 60
10 5 50
12 6 55

1
12