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 $sink$.

Constraints

* $2 \leq |V| \leq 100$
* $1 \leq |E| \leq 1000$
* $0 \leq c_i \leq 10000$

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.

Example

Input

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


Output

3
class edge:
    def __init__(self,to,cap,rev):
        self.to,self.cap,self.rev=to,cap,rev

def makeG(n):
    return [[] for _ in xrange(n)]

def add(G,fr,to,cap):
    G[fr].append(edge(to,cap,len(G[to])))
    G[to].append(edge(fr,0,len(G[fr])-1))

def dfs(G,v,t,f,used):
    if v==t: return f
    used[v]=True
    for i in xrange(len(G[v])):
        e=G[v][i]
        if not used[e.to] and e.cap>0:
            d=dfs(G,e.to,t,min(f,e.cap),used)
            if d>0:
                e.cap-=d
                G[e.to][e.rev].cap+=d
                return d
    return 0
    
def max_flow(G,n,s,t):
    flow=0
    while True:
        used=[False]*n
        f=dfs(G,s,t,float("inf"),used)
        if f==0: return flow
        flow+=f

V,E=map(int,raw_input().split())
G=makeG(V)
for i in xrange(E):
    u,v,c=map(int,raw_input().split())
    add(G,u,v,c)
s=0
t=V-1
print(max_flow(G,V,s,t))