Problem2566--Traffic Jams in the Land

2566: Traffic Jams in the Land

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Some country consists of (n+1) cities, located along a straight highway. Let's number the cities with consecutive integers from 1 to n+1 in the order they occur along the highway. Thus, the cities are connected by n segments of the highway, the i-th segment connects cities number i and i+1. Every segment of the highway is associated with a positive integer ai>1 − the period of traffic jams appearance on it.

In order to get from city x to city y (x<y), some drivers use the following tactics.

Initially the driver is in city x and the current time t equals zero. Until the driver arrives in city y, he perfors the following actions:

  • if the current time t is a multiple of ax, then the segment of the highway number x is now having traffic problems and the driver stays in the current city for one unit of time (formally speaking, we assign t=t+1);
  • if the current time t is not a multiple of ax, then the segment of the highway number x is now clear and that's why the driver uses one unit of time to move to city x+1 (formally, we assign t=t+1 and x=x+1).

You are developing a new traffic control system. You want to consecutively process q queries of two types:

  1. determine the final value of time t after the ride from city x to city y (x<y) assuming that we apply the tactics that is described above. Note that for each query t is being reset to 0.
  2. replace the period of traffic jams appearing on the segment number x by value y (formally, assign ax=y).

Write a code that will effectively process the queries given above.

Input

The first line contains a single integer n (1≤n≤105) − the number of highway segments that connect the n+1 cities.

The second line contains n integers a1,a2,...,an (2≤ai≤6) − the periods of traffic jams appearance on segments of the highway.

The next line contains a single integer q (1≤q≤105) − the number of queries to process.

The next q lines contain the descriptions of the queries in the format c, x, y (c − the query type).

If c is character 'A', then your task is to process a query of the first type. In this case the following constraints are satisfied: 1≤x<y≤n+1.

If c is character 'C', then you need to process a query of the second type. In such case, the following constraints are satisfied: 1≤x≤n, 2≤y≤6.

Output

For each query of the first type output a single integer − the final value of time t after driving from city x to city y. Process the queries in the order in which they are given in the input.

Examples
Input
10
2 5 3 2 3 5 3 4 2 4
10
C 10 6
A 2 6
A 1 3
C 3 4
A 3 11
A 4 9
A 5 6
C 7 3
A 8 10
A 2 5
Output
5
3
14
6
2
4
4

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