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 \gt 1 - the period of traffic jams appearance on it.

In order to get from city x to city y (x \lt 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:
determine the final value of time t after the ride from city x to city y (x \lt y) assuming that we apply the tactics that is described above. Note that for each query t is being reset to 0. 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.

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

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

The next line contains a single integer q (1 \le q \le 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 \le x \lt y \le 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 \le x \le n, 2 \le y \le 6.

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.