Problem:
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Maximum Flow

A flow network is a directed graph which has a $source$ and a $sink$. In a flow network, each edge $(u, v)$ has a capacity $c(u, v)$. Each edge receives a flow, but the amount of flow on the edge can not exceed the corresponding capacity. Find the maximum flow from the $source$ to the $sink$.

Input

A flow network is given in the following format.

$|V|\;|E|$

$u_0\;v_0\;c_0$

$u_1\;v_1\;c_1$

:

$u_{|E|-1}\;v_{|E|-1}\;c_{|E|-1}$

$|V|$, $|E|$ is the number of vertices and edges of the flow network respectively. The vertices in $G$ are named with the numbers 0, 1,..., $|V|-1$. The source is 0 and the sink is $|V|-1$.

$u_i$, $v_i$, $c_i$ represent $i$-th edge of the flow network.
A pair of $u_i$ and $v_i$ denotes that there is an edge from $u_i$ to $v_i$ and $c_i$ is the capacity of $i$-th edge.

Output

Print the maximum flow.

Constraints

$2 \leq |V| \leq 100$

$1 \leq |E| \leq 1000$

$0 \leq c_i \leq 10000$

Sample Input 1

4 5
0 1 2
0 2 1
1 2 1
1 3 1
2 3 2

Sample Output 1

3

Solution in Python3 (judge verdict: Wrong Answer)

import sys
sys.setrecursionlimit(200000)
n,e = map(int,input().split())
g = [[] for i in range(n)]
for i in range(e):
  a,b,c = map(int,input().split())
  g[a].append([b,c,0])
def dfs(x,t,f):
  if x == t:
    return f
  global used
  used[x] = 1
  for j in range(len(g[x])):
    y, cap, rev = g[x][j]
    if cap and not used[y]:
      d = dfs(y,t,min(f,cap))
      if d:
        g[x][j][1] -= d
        g[x][j][2] += d
        return d
  return 0

flow = 0
f = INF = float("inf")
while f:
  used = [0]*n
  f = dfs(0,n-1,INF)
  flow += f
  
print(flow)