Problem Statement

Thermostat Control Aryan's thermostat starts switched off at temperature `0`. At any whole minute he may set it to heating, cooling, or off. Heating changes the temperature by `+1` per minute, cooling by `-1` per minute, and off leaves it unchanged. There are friends arriving at specified minutes. Friend `i` is comfortable only if the temperature at minute `t[i]` is between `l[i]` and `r[i]`, inclusive. Determine whether all friends can be made comfortable. Input The first line contains `T`, the number of test cases. Each test case starts with `n` (`1 <= n <= 2*10^5`). Then follow `n` lines with `t[i]`, `l[i]`, and `r[i]`; times are non-decreasing. The sum of `n` over all test cases does not exceed `2*10^5`. Output For every test case print `YES` if a valid schedule exists, otherwise print `NO`. Notes The temperature can be changed by at most one per minute. Multiple friends may arrive at the same minute, so all of their ranges must contain one common temperature.