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Difficulty Level: Hard

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Find the Maximum Flow
     

Given a graph with N vertices numbered 1 to N and M edges, the task is to find the max flow from vertex 1 to vertex N.

Input:
The first line of input contains an integer T denoting the no of test cases. Then T test cases follow. The first line of each test case contains two space separated integers N and M . Then in the next line are M space separated triplets x, y, z denoting an undirected edge from x to y with a flow capacity of z.

Output:
For each test case in a new line print a single integer denoting the maximum flow between 1 to N.

Constraints:
1<=T<=100
1<=N,M<=1000

Example:
Input:

2
5 4
1 2 1 3 2 2 4 2 3 2 5 5
4 4
1 2 8 1 3 10 2 4 2 3 4 3
Output:
1
5

** For More Input/Output Examples Use 'Expected Output' option **

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