Travel Time Queries

You are given a sequence of travel times between consecutive checkpoints along a route. The checkpoints are numbered from 1 to \( n \) and there are exactly \( n-1 \) travel time values. Your task is to implement a class TravelTime that supports the following operations:

1. Query Type 1: Given two checkpoints \( x \) and \( y \) (with \( x < y \)), return the total travel time (i.e. the sum of travel times) from checkpoint \( x \) to checkpoint \( y \).
2. Query Type 2: Update the travel time between checkpoint \( x \) and checkpoint \( x+1 \) to a new value \( t \).

Additionally, you need to implement a helper function process_queries that reads a list of queries and outputs the results of Query Type 1. When a Query Type 2 is encountered, update the travel times accordingly before processing further queries. The internal implementation may use a prefix sum strategy to compute ranges efficiently. Note that whenever an update occurs, the prefix sum should be recalculated.

inputFormat

The input is provided via stdin and follows this format:

• The first line contains an integer n representing the total number of checkpoints.
• The second line contains \( n-1 \) integers representing the travel times between consecutive checkpoints.
• The third line contains an integer q representing the number of queries.
• The next q lines each describe a query in one of the following formats:
  • 1 x y: Query Type 1 – output the sum of travel times from checkpoint x to y.
  • 2 x t: Query Type 2 – update the travel time between checkpoint x and x+1 to t.

outputFormat

For each Query Type 1, output the computed total travel time on a new line via stdout. Queries of Type 2 do not produce any output.

## sample

5
3 2 4 5
4
1 1 5
2 2 3
1 1 3
1 3 5

14
6
9

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