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Sines Sum Queries

Problem code: SINSUMQ

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You are given a sequence of integers A0, A1, ..., AN-1. Initially Ai=i for all i. You need to perform some strange queries with it. Each query has the form "L R D" where 0 <= L <= R < N and D is an integer. If D=0 then you need to find the sum of sines of the numbers AL, AL+1, ..., AR that is sin AL + ... + sin AR. Otherwise you need to add D to the numbers AL, AL+1, ..., AR.

Input

The first line contains two positive integers N and Q. Here, N <= 109 is the length of the initial sequence and Q <= 100000 is the number of queries you need to perform with it. The next Q lines describe queries, one per line. The i'th such line contains three integers L, R and D. Here 0 <= L <= R < N and -10000 <= D <= 10000.

Output

The output consists of answers for all queries where D=0. For each such query you must produce a line with the corresponding sines sum. Answers within an absolute error of 10-6 will be accepted.

Example

Input:
5 6
0 4 0
0 2 1
3 4 2
0 4 0
2 3 -1
1 4 0

Output:
1.1350859
0.65354865
0.782376860

Date:2011-06-08
Time limit:7s
Source limit:50000B
Languages:All


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Program should read from standard input and write to standard output.

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