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
#include <bits/stdc++.h>
const int M = 60;
const int N = 100000 + 5;
struct SegmentTree {
  int t[N << 2][M];
  void up(int rt) {
    for (int i = 0; i < 60; ++i) {
      t[rt][i] = t[rt << 1 | 1][(t[rt << 1][i] + i) % M] + t[rt << 1][i];
    }
  }
  void modify(int p, int dt, int l, int r, int rt) {
    if (l == r) {
      for (int i = 0; i < M; ++i) {
        if (i % dt == 0) {
          t[rt][i] = 2;
        } else {
          t[rt][i] = 1;
        }
      }
      return;
    }
    int mid = l + r >> 1;
    if (p <= mid)
      modify(p, dt, l, mid, rt << 1);
    else
      modify(p, dt, mid + 1, r, rt << 1 | 1);
    up(rt);
  }
  int query(int L, int R, int d, int l, int r, int rt) {
    if (L <= l && r <= R) {
      return d + t[rt][d % M];
    }
    int mid = l + r >> 1;
    if (L <= mid) d = query(L, R, d, l, mid, rt << 1);
    if (mid < R) d = query(L, R, d, mid + 1, r, rt << 1 | 1);
    return d;
  }
} sgt;
int n, m;
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) {
    int x;
    scanf("%d", &x);
    sgt.modify(i, x, 1, n, 1);
  }
  scanf("%d", &m);
  while (m--) {
    char op[2];
    int a, b;
    scanf("%s%d%d", op, &a, &b);
    if (op[0] == 'C') {
      sgt.modify(a, b, 1, n, 1);
    } else {
      printf("%d\n", sgt.query(a, b - 1, 0, 1, n, 1));
    }
  }
  return 0;
}
