Animesh has $n$ empty candy jars, numbered from ${1}$ to $n$, with infinite capacity. He performs $m$ operations. Each operation is described by $3$ integers, ${a}$, ${b}$, and ${k}$. Here, ${a}$ and ${b}$ are indices of the jars, and ${k}$ is the number of candies to be added inside each jar whose index lies between ${a}$ and ${b}$ (both inclusive).
Can you tell the average number of candies after $m$ operations?

Example

$n=5$

$operations=[[1,2,10],[3,5,10]]$

The array has $5$ elements that all start at ${0}$. In the first operation, add $10$ to the first $2$ elements. Now the array is $[10,10,0,0,0]$. In the second operation, add $10$ to the last $3$ elements (3 - 5). Now the array is $[10,10,10,10,10]$ and the average is 10. Sincd 10 is already an integer value, it does not need to be rounded.

Function Description

Complete the solve function in the editor below.

solve has the following parameters:

int n: the number of candy jars
int operations[m][3]: a 2-dimensional array of operations

Returns

int: the floor of the average number of canidies in all jars

Input Format

The first line contains two integers, $n$ and $m$, separated by a single space.

$m$ lines follow. Each of them contains three integers, ${a}$, ${b}$, and ${k}$, separated by spaces.

Constraints

$3\leq n\leq10^7$

$1\leq m\leq10^5$

$1\leq a\leq b\leq N$

$0\leq k\leq10^6$

Sample Input
STDIN Function
----- --------
5 3 n = 5, operations[] size = 3
1 2 100 operations = [[1, 2, 100], [2, 5, 100], [3, 4, 100]]
2 5 100
3 4 100

Sample Output
160

Explanation

Initially each of the jars contains 0 candies

0 0 0 0 0

First operation:

100 100 0 0 0

Second operation:

100 200 100 100 100

Third operation:

100 200 200 200 100

Total = 800, Average = 800/5 = 160

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