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## FLOW - Maximum Flow

Given a graph with n (2 ≤ n ≤ 50) vertices numbered 1 to n and m (1 ≤ m ≤ 1000) directed, weighted edges, compute the maximum flow  from vertex 1 to vertex n.

### Input

The first line contains the two integers n and m. The next m lines each contain three integers u, v, and c, denoting that there is an edge (u,v) of capacity c, where 1 ≤ c ≤ 1000 and 1 ≤ u, v ≤ n.

### Output

Output the value of the maximum flow from 1 to n.

### Example

```Input:
4 5
1 2 3
1 3 4
2 4 4
3 2 1
3 4 2

Output: 6```

 Added by: Thomas Thierauf Date: 2012-04-12 Time limit: 0.208s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All except: ASM32-GCC ASM64 MAWK BC C-CLANG CPP14-CLANG CPP14 COBOL COFFEE D-DMD D-CLANG DART ELIXIR FANTOM FORTH GOSU GRV JS-MONKEY KTLN NIM NODEJS OBJC OBJC-CLANG OCT PICO PROLOG PYPY PY_NBC R RACKET RUST CHICKEN SQLITE SWIFT UNLAMBDA VB.NET