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 Ruby (judge verdict: Accepted)

nv, ne = gets.split.map(&:to_i)

to = []
nv.times do to << [] end

ne.times do 
    u, v, c = gets.split.map(&:to_i)
    to[u] << [v, c, to[v].size]
    to[v] << [u, 0, to[u].size-1]
end

def dfs(to, seen, u, t, f)
    return f if u == t
    seen[u] = true
    to[u].each do |e|
        v, c, rev = e
        next if seen[v] or c == 0
        d = dfs(to, seen, v, t, [f, c].min)
        next if d == 0
        e[1] -= d
        to[v][rev][1] += d
        return d
    end
    return 0
end

ans = 0
while true
    seen = Array.new(nv, false)
    f = dfs(to, seen, 0, nv-1, 10005)
    if f == 0
        puts ans
        break
    else
        ans += f
    end
end