Starting with a 1-indexed array of zeros and a list of operations, for each operation add a value to each the array element between two given indices, inclusive. Once all operations have been performed, return the maximum value in the array.

Example

$n=10$

$queries=[[1,5,3],[4,8,7],[6,9,1]$

Queries are interpreted as follows:

a b k
1 5 3
4 8 7
6 9 1

Add the values of $\boldsymbol{\mbox{k}}$ between the indices $\class{ML__boldsymbol}{\boldsymbol{a}}$ and $\boldsymbol{b}$ inclusive:

index-> 1 2 3 4 5 6 7 8 9 10
[0,0,0, 0, 0,0,0,0,0, 0]
[3,3,3, 3, 3,0,0,0,0, 0]
[3,3,3,10,10,7,7,7,0, 0]
[3,3,3,10,10,8,8,8,1, 0]

The largest value is $10$ after all operations are performed.

Function Description

Complete the function arrayManipulation in the editor below.

arrayManipulation has the following parameters:

int n - the number of elements in the array
int queries[q][3] - a two dimensional array of queries where each queries[i] contains three integers, a, b, and k.

Returns

int - the maximum value in the resultant array

Input Format

The first line contains two space-separated integers $n$ and $m$, the size of the array and the number of operations.

Each of the next $m$ lines contains three space-separated integers $\class{ML__boldsymbol}{\boldsymbol{a}}$, $\boldsymbol{b}$ and $\boldsymbol{\mbox{k}}$, the left index, right index and summand.

Constraints

$3\leq n\leq10^7$
$1\leq m\leq2*10^5$
$1\leq a\leq b\leq n$
$0\leq k\leq10^9$

Sample Input
5 3
1 2 100
2 5 100
3 4 100

Sample Output
200

Explanation

After the first update the list is 100 100 0 0 0.

After the second update list is 100 200 100 100 100.

After the third update list is 100 200 200 200 100.

The maximum value is $\textbf{200}$.

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