human
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
Using python3 can you solve the prior task?
 ... What is a Python code to find the maximum flow from the $source$ to the $sink$?
assistant
#Here is Python code to find the maximum flow from the $source$ to the $sink$.

from collections import deque

class Dinic:
    def __init__(self, N):
        self.N = N
        self.E = [[] for _ in range(N)]
    
    def add_edge(self, init, end, capacity):
        '''
            e[0] = the head vertex of e,
            e[1] = current capacity of e,
            e[2] = the index of reverse edge of e.
        '''
        self.E[init].append([end, capacity, len(self.E[end])])
        self.E[end].append([init, 0, len(self.E[init]) - 1])
    
    def _exist_augpath(self, s, t):
        self.level = level = [-1] * self.N # the level (depth) of each vertex
        E = self.E
        q = deque([(s, 0)]) # (vertex, level)
        while q:
            v, lv = q.popleft()
            if level[v] < 0: # visited v for the first time
                level[v] = lv
                for u, cap, _ in E[v]:
                    if cap == 0 or level[u] >= 0: continue
                    q.append((u, lv + 1))
        return level[t] >= 0
    
    def _blocking_flow(self, s, t):
        aug_flow = 0
        finished = [False] * self.N
        parent = [-1] * self.N
        revs = [-1] * self.N
        bottleneck = -1; temp_flow = 0
        E, level = self.E, self.level
        stack = [(s, -1, float('inf'), -1, 0)] # (vertex, parent, flow, rev_idx, status)
        while stack:
            v, p, f, rev, st = stack.pop()
            if temp_flow and v != bottleneck: continue
            if st == 0 and not finished[v]:
                parent[v] = p; revs[v] = rev
                if temp_flow: # offset
                    f -= temp_flow; temp_flow = 0; bottleneck = -1
                if v == t: # an augment path is found
                    aug_flow += f
                    if p != -1: stack += [(v, p, f, rev, 3)]
                    continue
                n_children = 0
                for u, cap, rev_idx in E[v]:
                    if cap == 0 or finished[u] or level[u] != level[v] + 1: continue
                    if n_children == 0:
                        stack += [(v, p, 0, rev, 2), (u, v, min(f, cap),...