#include <bits/stdc++.h>
#define For(i,a,b) for(int i=a;i<=b;i++)
#define Rev(i,a,b) for(int i=a;i>=b;i--)
#define Fin(file) freopen(file,"r",stdin)
#define Fout(file) freopen(file,"w",stdout)
using namespace std; using ll = long long;
#define printf(...) (0==0)
const int N=2e6+5;
class DSU{
public:
	int n,fa[N];
	void init(int _n) { n=_n; iota(fa+1,fa+1+n,1); }
	int getfa(int x) { return x==fa[x]?x:fa[x]=getfa(fa[x]); }
}S;
char ss[N]; int n,K,fa[N],lis[N],lcnt,tmp[N],tcnt,g[N]; vector<int> to[N],son[N]; ll f[N][2],Ans[N];
void dfs0(int u,int pa) { fa[u]=pa; lis[++lcnt]=u; for(int v:to[u]) if(v!=pa) son[u].push_back(v),dfs0(v,u); }
int main(){
	//~ Fin("hh.in"); Fout("hh.out");
	cin>>n>>(ss+1); For(i,1,n-1) { int x,y; cin>>x>>y; to[x].push_back(y); to[y].push_back(x); }
	dfs0(1,0); S.init(n); int Dlt=0;
	for(K=1;K<=n;K++){
		//~ if(K==5){
			//~ printf("K=5\n");
			//~ For(i,1,lcnt){
				//~ printf("lis[%d]=%d\n",i,lis[i]);
				//~ for(int v:son[lis[i]]) printf("%d ",v);; puts("");
			//~ }
		//~ }
		Rev(i,lcnt,1){
			int u=lis[i];
			f[u][1]=1; f[u][0]=(ss[u]=='0'?0:1e18);
			for(int v:son[u]){
				ll f1 = min( f[u][1]+f[v][1], f[u][1]+f[v][0] );
				ll f0 = min( f[u][0]+f[v][1]+K, f[u][0]+f[v][0] );
				f[u][1]=f1; f[u][0]=f0;
			}
		}
		Ans[K]=min(f[1][0],f[1][1]+K)+Dlt;
		g[1] =  f[1][0]<f[1][1]+K ? 0 : 1;
		tcnt=0; tmp[++tcnt]=1;
		For(i,1,lcnt) if(son[lis[i]].size()){
			int u=lis[i];
			for(int v:son[u]){
				if(g[u]==1) g[v] = f[u][1]+f[v][1]<f[u][1]+f[v][0] ? 1 : 0;
				else g[v] = f[u][0]+f[v][1]+K<f[u][0]+f[v][0] ? 1 : 0;
				if(g[v]==1&&g[u]==1) S.fa[v]=S.getfa(fa[v]),Dlt++,ss[u]='1',printf("K=%d: Deleted %d\n",K,v);
				else tmp[++tcnt]=v;
			}
		}
		For(i,1,lcnt) son[lis[i]].clear();
		lcnt=tcnt; For(i,1,lcnt) lis[i]=tmp[i];
		For(i,2,lcnt) son[S.getfa(fa[lis[i]])].push_back(lis[i]);
	}
	For(i,1,n) cout<<Ans[i]<<'\n';
	return 0;
}