A sensor reports every hour, except when it does not. Downstream wants a reading on every row, so a gap takes the last value the sensor actually sent.

Input

Rows do not arrive in timestamp order.

Output

One row for every input row, same sensor_id and reading_ts, with:

• reading_c — the reading if there is one, otherwise the most recent non-null reading from the same sensor at an earlier timestamp, and null if that sensor has not reported yet

Example

Constraints

• Forward only. A later reading never fills an earlier gap — that would put a value into a row that could not have known it.
• Sensors are independent. One sensor never fills another's gap.
• Leading nulls stay null. There is nothing to carry forward yet, and inventing a zero there is a reading that was never taken.
• Row order is not graded. Column names and their order are.