网络流+先跑一遍确保正确性：ARC156F

https://www.luogu.com.cn/problem/AT_arc156_f

可以很显然建一个流：

然而它最大流是对的，但构造方案可能会假，因为存在最左边的边没流，相当于某个数没选。

一定有解是怎样？全选 $a_i$，所以我们可以先全选 $a_i$ 跑。然后我们再加入 $b_i,c_i$ 来跑，那样反悔一定不会反悔到最左边的边上。

pre coding at 21:01
st coding at 21:11
st bugging at 21:18
passing at 21:25
fn blogging at 21:33

#include<bits/stdc++.h>
using namespace std;
#ifdef LOCAL
 #define debug(...) fprintf(stdout, ##__VA_ARGS__)
#else
 #define debug(...) void(0)
#endif
//#define int long long
inline int read(){int x=0,f=1;char ch=getchar(); while(ch<'0'||
ch>'9'){if(ch=='-')f=-1;ch=getchar();}while(ch>='0'&&ch<='9'){
x=(x<<1)+(x<<3)+(ch^48);ch=getchar();}return x*f;}
#define Z(x) (x)*(x)
#define pb push_back
#define fi first
#define se second
//srand(time(0));
#define N 400010
//#define M
//#define mo
namespace Flow {
	#define int long long
	struct mf_graph {
		struct node {
			int x, y, z, n; 
		}; 
		vector<node>d; 
		vector<int>h, H, dep; 
		queue<int>q; 
		int k; 
		int u, v, w, S, T, ans=0; 
		void reset(int n) {
			h.resize(n+5); k=1; d.resize(2); 
			H.resize(n+5); dep.resize(n+5); 
		}
		void cun(int x, int y, int z) {
			++k; d.pb({x, y, z, h[x]}); 
			d[k].n=h[x]; h[x]=k;
		}
		int add_edge(int x, int y, int z) {
        	// debug("%lld -> %lld %lld\n", x, y, z); 
			cun(x, y, z); cun(y, x, 0); 
			return k-1; 
		}
		int get_edge(int k) { return d[k].z; }
		int bfs() {
			while(!q.empty()) q.pop(); 
			fill(dep.begin(), dep.end(), -1); 
			h=H; 
			dep[S]=1; q.push(S); 
			while(!q.empty()) {
				u=q.front(); q.pop(); 
				for(int g=h[u]; g; g=d[g].n) {
					v=d[g].y; w=d[g].z; 
					if(w<=0 || dep[v]!=-1) continue; 
					dep[v]=dep[u]+1; q.push(v); 
				}
			}
			return dep[T]!=-1; 
		}
		int dfs(int x, int w) {
			if(x==T) return w;
			if(!w) return 0; 
			int ans=0, s; 
			for(int &i=h[x]; i; i=d[i].n) {
				int y=d[i].y, z=d[i].z;  
				if(dep[y]!=dep[x]+1) continue; 
				if(z<=0) continue; 
				s=dfs(y, min(w, z)); ans+=s; w-=s; 
				d[i].z-=s; d[i^1].z+=s; 
				if(!w) break;  
			}
			return ans; 
		}
		int flow(int SS, int TT) {
			S=SS; T=TT; H=h; ans=0; 
			while(bfs()) ans+=dfs(S, 1e18); 
			return ans; 
		}
	}; 	
	#undef int
}
using namespace Flow; 
int n, m, i, j, k, T, S, tot;
int ans, L[N], R[N], a[N], p1[N], p2[N], qr[N]; 

signed main()
{
	#ifdef LOCAL
	  freopen("in.txt", "r", stdin);
	  freopen("out.txt", "w", stdout);
	#endif
//	T=read();
//	while(T--) {
//
//	}
	mf_graph G; G.reset(4e5); 
	n = read(); S = 1; T = tot = 2; 
	for(i=1; i<=1e5; ++i) L[i]=++tot, R[i]=++tot, qr[i]=G.add_edge(L[i], R[i], 1); 
	for(i=1; i<=n; ++i) {
		p1[i]=++tot, p2[i]=++tot; 
		G.add_edge(S, p1[i], 1); 
		G.add_edge(p2[i], T, 1); 
	}
	for(i=1; i<=n; ++i) {
		a[i]=read(); 
		G.add_edge(p1[i], L[a[i]], 1); 
		G.add_edge(R[a[i]], p2[i], 1); 
	}
	ans = G.flow(S, T); 
//	debug("%d\n", ans); 
	for(i=1; i<=n; ++i) {
		a[i]=read(); 
		G.add_edge(p1[i], L[a[i]], 1); 
//		G.add_edge(R[a[i]], p2[i], 1); 
	}
	for(i=1; i<=n; ++i) {
		a[i]=read(); 
//		G.add_edge(p1[i], L[a[i]], 1); 
		G.add_edge(R[a[i]], p2[i], 1); 
	}
	ans += G.flow(S, T); 
	printf("%d\n", ans); 
	for(i=1; i<=1e5; ++i) {
		k = G.get_edge(qr[i]); 
		if(!k) printf("%d ", i); 
	}
	return 0;
}