D — Drainage Ditches

Every time it rains on Farmer John's fields, a pond forms over Bessie's favorite clover patch. This means that the clover is covered by water for a while and takes quite a long time to regrow. Thus, Farmer John has built a set of drainage ditches so that Bessie's clover patch is never covered in water. Instead, the water is drained to a nearby stream. Being an ace engineer, Farmer John has also installed regulators at the beginning of each ditch, so he can control the rate at which water flows into that ditch.

Farmer John knows not only how many gallons of water each ditch can transport per minute but also the exact layout of the ditches, which feed out of the pond, run into each other, and lead into the stream, in a potentially complex network.

Given all this information, determine the maximum rate at which water can be transported out of the pond and into the stream. For any given ditch, water flows in only one direction, but there might be a way that water can flow in a circle.

Input Specification

The input consists of several test cases. For each case, the first line contains two space-separated integers N (0 ≤ N ≤ 200) and M (2 ≤ M ≤ 200). N is the number of ditches that Farmer John has dug. M is the number of intersections points for those ditches. Intersection point 1 is the pond. Intersection point M is the stream. Each of the following N lines contains three integers S_i, E_i, and C_i. S_i and E_i (1 ≤ S_i, E_i ≤ M) designate the intersections between which ditch i is located. Water will flow through this ditch from S_i to E_i. C_i (0 ≤ C_i ≤ 10 000 000) is the maximum rate at which water will flow through the ditch.

Output Specification

For each test case, output a single integer: the maximum rate at which water may be emptied from the pond.

Sample Input

1. 5 4
2. 1 2 40
3. 1 4 20
4. 2 4 20
5. 2 3 30
6. 3 4 10

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Output for Sample Input

1. 50

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