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///Max Flow Push-relabel improved
///O(N*M+N*N*sqrt(M))
#include <bits/stdc++.h>
using namespace std;
ifstream f("maxflow.in");
ofstream g("maxflow.out");
const int NMAX=1005,INF=0x3F3F3F3F;
int n,m,x,y,c;
struct flux
{
int flow,capacity;
} graph[NMAX][NMAX];
vector<int>height,excess;
void push(int node,int next)
{
int new_flow=min(excess[node],graph[node][next].capacity-graph[node][next].flow);
graph[node][next].flow+=new_flow;///update on the normal edge
graph[next][node].flow-=new_flow;///update on the reverse edge
excess[node]-=new_flow;///update on the current node
excess[next]+=new_flow;///update on the next node
}
void relabel(int node)
{
int min_h=INF;
for(int i=1; i<=n; i++)
if(graph[node][i].capacity-graph[node][i].flow>0)///meaning we can still push flow through this edge
min_h=min(min_h,height[i]);
if(min_h!=INF)
height[node]=min_h+1;
}
inline vector<int>find_max_height_nodes(int s,int t)
{
vector<int>max_height;
for(int node=1; node<=n; node++)
if(node!=s && node!=t && excess[node]>0)
{
if(!max_height.empty() && height[node]>height[max_height[0]])///we found a new maximum
max_height.clear();
if(max_height.empty() || height[node]==height[max_height[0]])///we update the vector with the nodes which have a maximum height
max_height.push_back(node);
}
return max_height;
}
int maxflow(int s,int t)
{
int max_flow=0;
height.assign(n+1,0);
height[s]=n+1;
excess.assign(n+1,0);
excess[s]=INF;
for(int i=1; i<=n; i++)
if(graph[s][i].capacity>0)///if we have an edge between s and i we should push
push(s,i);
vector<int>current=find_max_height_nodes(s,t);///returns a vector with the nodes which have excess and a maximum height
while(!current.empty())///there are nodes with excess and maximum height
{
for(int i=0; i<current.size(); i++)
{
int node=current[i];
bool pushed=0;
for(int next=1; next<=n && excess[node]>0; next++)
{
if(graph[node][next].capacity-graph[node][next].flow>0 && height[node]==height[next]+1)
{
push(node,next);
pushed=1;
}
}
if(!pushed)
{
relabel(node);
break;
}
}
current=find_max_height_nodes(s,t);///returns a vector with the nodes which have excess and a maximum height
}
for(int i=1; i<=n; i++)
max_flow+=graph[i][t].flow;///if there is no edge,the flow will be 0
return max_flow;
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
f>>n>>m;
for(int i=1; i<=m; i++)
{
f>>x>>y>>c;
graph[x][y].capacity=c;///graph[x][y].flow=0 already
}
g<<maxflow(1,n);///source, terminal
return 0;
}