An industrial actuator ships with a single-use firing latch: the very first activation request it receives causes it to fire and report a computed value, but every activation after that finds the latch already spent and reports nothing new. Each activation request carries a list of integer sensor readings. Simulate the actuator across every request it receives, in the order the requests arrive, and report what it outputs for each one.

Input format

Line 1: an integer q — the number of activation requests. Each of the next q lines describes one request: an integer k followed by k space-separated integers r_1..r_k, the sensor readings carried by that request. If k is 0, the line contains only the value 0 (an empty reading list).

Output format

Print q lines. For the first request (earliest in input order), print the sum of its sensor readings. For every request after the first, print the single word LATCHED (uppercase, no quotes) — the actuator has already fired and ignores that request's readings entirely, regardless of what they are.

Constraints

• 1 <= q <= 10^5
• 0 <= k <= 20 for each request
• -1000 <= r_i <= 1000

3
3 1 2 3
2 5 5
0

6
LATCHED
LATCHED

1
0

0