RACETIME - Race Against Time


As another one of their crazy antics, the N (1 ≤ N ≤ 100,000) cows want Farmer John to race against the clock to answer some of their pressing questions.

The cows are lined up in a row from 1 to N, and each one is holding a sign representing a number, Ai (1 ≤ Ai ≤ 1,000,000,000). The cows need FJ to perform Q (1 ≤ Q ≤ 50,000) operations, which can be either of the following:

  • Modify cow i's number to X (1 ≤ X ≤ 1,000,000,000). This will be represented in the input as a line containing the letter M followed by the space-separated numbers i and X.
  • Count how many cows in the range [P, Q] (1 ≤ P ≤ Q ≤ N) have Ai ≤ X (0 ≤ X ≤ 1,000,000,000). This will be represented in the input as a line containing the letter C followed by the space-separated numbers P, Q, and X.

Of course, FJ would like your help.

Input

The first line gives the integers N and Q, and the next N lines give the initial values of Ai. Finally, the next Q lines each contain a query of the form "M i X" or "C P Q X".

Output

Print the answer to each 'C' query, one per line.

Example

Input:
4 6
3
4
1
7
C 2 4 4
M 4 1
C 2 4 4
C 1 4 5
M 2 10
C 1 3 9

Output:
2
3
4
2

FJ has 4 cows, whose initial numbers are 3, 4, 1, and 7. The cows then give him 6 operations; the first asks him to count the how many of the last three cows have a number at most 4, the second asks him to change the fourth cow's number to 1, etc.

Warning: large input/output data.

hide comments
sarwar__05: 2019-07-15 09:35:48

similar to GIVEAWAY

a_ranjan: 2019-06-21 10:14:34

Holy F*** ! My sqrt decomposition code got TLE and N*Q brute forciiiiiie got AC . Hahhahaha!!!!

kshubham02: 2019-04-21 21:20:56

N*log^2(N) times out.
Brute force in N*Q passes.
????????????????

aimbot: 2018-01-10 19:23:33

very good problem

Last edit: 2018-01-10 19:23:58
mamnoonsiam: 2017-11-04 01:15:40

@mathecodician I am gonna say you that my O(10e9 * NQ) passed. :) B)

mathecodician: 2017-09-20 18:01:07

Here people are talking about N*log^2(N) not passing but my NQ passed lol

saurabh0605: 2017-09-17 08:07:24

Is there any tutorial for this problem?

bthero_03: 2017-06-08 08:58:08

Easy problem. My complexity is N + q * sqrt(n) * log(n).

secta: 2016-03-02 14:00:48

I couldn't make my N*log^2(N) pass, I used segment tree with treap in each node and added fast input but still TLE :(

Junior Andrade [UNIFEI]: 2015-10-09 18:54:10

N + q*sqrt(n)*log(n) works! :)


Added by:Neal Wu
Date:2008-10-25
Time limit:0.155s-1.242s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO