#include<bits/stdc++.h>
using namespace std;
namespace my_std{
	#define ll long long
	#define bl bool
	ll my_pow(ll a,ll b,ll mod){
		ll res=1;
		if(!b) return 1;
		while(b){
			if(b&1) res=(res*a)%mod;
			a=(a*a)%mod;
			b>>=1;
		}
		return res;
	}
	ll qpow(ll a,ll b){
		ll res=1;
		if(!b) return 1;
		while(b){
			if(b&1) res*=a;
			a*=a;
			b>>=1;
		}
		return res;
	}
	#define db double
	#define pf printf
	#define pc putchar
	#define fr(i,x,y) for(register ll i=(x);i<=(y);i++)
	#define pfr(i,x,y) for(register ll i=(x);i>=(y);i--)
	#define go(u) for(ll i=head[u];i;i=e[i].nxt)
	#define enter pc('\n')
	#define space pc(' ')
	#define fir first
	#define sec second
	#define MP make_pair
	#define il inline
	#define inf 1e9
	#define random(x) rand()*rand()%(x)
	#define inv(a,mod) my_pow((a),(mod-2),(mod))
	il ll read(){
		ll sum=0,f=1;
		char ch=0;
		while(!isdigit(ch)){
			if(ch=='-') f=-1;
			ch=getchar();
		}
		while(isdigit(ch)){
			sum=sum*10+(ch^48);
			ch=getchar();
		}
		return sum*f;
	}
	il void write(ll x){
		if(x<0){
			x=-x;
			pc('-');
		}
		if(x>9) write(x/10);
		pc(x%10+'0');
	}
	il void writeln(ll x){
		write(x);
		enter;
	}
	il void writesp(ll x){
		write(x);
		space;
	}
}
using namespace my_std;
vector<ll> vec[200020];
ll n,fa[200020],son[200020],pre[200020],suf[200020],w[200020];
ll siz[200020],st[200020],top=0,dp[200020][2];
char s[200020];
bl ck[200020];
void dfs0(ll u){
	ll lst=0;
	siz[u]=1;
	fr(i,0,(ll)vec[u].size()-1){
		ll v=vec[u][i];
		if(v==fa[u]) continue;
		fa[v]=u;
		if(lst){
			pre[v]=lst;
			suf[lst]=v;
		}
		else son[u]=v;
		dfs0(v);
		lst=v;
	}
}
void del(ll u,ll v){
	if(son[u]==v) son[u]=suf[v];
	if(pre[v]) suf[pre[v]]=suf[v];
	if(suf[v]) pre[suf[v]]=pre[v];
}
void ins(ll u,ll v){
	pre[son[u]]=v;
	suf[v]=son[u];
	pre[v]=0;
	son[u]=v;
	fa[v]=u;
}
void cut(ll u){
	for(ll v=son[u];v;v=suf[v]){
		cut(v);
		if(ck[v]) continue;
		if(!son[v]||!suf[son[v]]){
			ll vv=son[v];
			del(u,v);
			if(vv){
				ins(u,vv);
				w[vv]+=w[v]+siz[v];
			}
		}
	}
}
void dfs1(ll u,ll k){
	dp[u][0]=dp[u][1]=inf;
	ll sum0=0,sum1=0,minn=inf;
	for(ll v=son[u];v;v=suf[v]){
		dfs1(v,k);
		ll tmp=min(dp[v][0],dp[v][1]);
		sum0+=tmp;
		if((dp[v][1]+w[v]-k)<=tmp) sum1+=dp[v][1]+w[v]-tmp-k;
		minn=min(minn,dp[v][1]+w[v]-tmp-k);
	}
	dp[u][0]=sum0;
	dp[u][1]=sum0+siz[u]+k;
	if(minn<=0) dp[u][1]=min(dp[u][1],sum0+sum1+siz[u]+k);
	else dp[u][1]=min(dp[u][1],sum0+minn+siz[u]+k);
	if(ck[u]) dp[u][0]=inf;
}
void dfs2(ll u,ll col,ll k){
	ll sum0=0,sum1=0,minn=inf,pos;
	for(ll v=son[u];v;v=suf[v]){
		ll tmp=min(dp[v][0],dp[v][1]);
		sum0+=tmp;
		if((dp[v][1]+w[v]-k)<=tmp) sum1+=dp[v][1]+w[v]-tmp-k;
		if(minn>(dp[v][1]+w[v]-tmp-k)){
			minn=dp[v][1]+w[v]-tmp-k;
			pos=v;
		}
	}
	if(!col){
		for(ll v=son[u];v;v=suf[v]){
			if(dp[v][0]<=dp[v][1]) dfs2(v,0,k);
			else dfs2(v,1,k);
		}
	}
	else{
		if(dp[u][1]==(sum0+siz[u]+k)){
			for(ll v=son[u];v;v=suf[v]){
				if(dp[v][0]<=dp[v][1]) dfs2(v,0,k);
				else dfs2(v,1,k);
			}
		}
		else if(minn<=0){
			for(ll v=son[u];v;v=suf[v]){
				ll tmp=min(dp[v][0],dp[v][1]);
				if((dp[v][1]+w[v])<=tmp){
					dfs2(v,1,k);
					st[++top]=v;
				}
				else{
					if(dp[v][0]<=dp[v][1]) dfs2(v,0,k);
					else dfs2(v,1,k);
				}
			}
		}
		else{
			for(ll v=son[u];v;v=suf[v]){
				if(v==pos){
					dfs2(v,1,k);
					st[++top]=v;
				}
				else{
					if(dp[v][0]<=dp[v][1]) dfs2(v,0,k);
					else dfs2(v,1,k);
				}
			}
		}
	}
}
void print(ll u){
	pf("%lld %lld : %lld\n",fa[u],u,w[u]);
	for(ll v=son[u];v;v=suf[v]) print(v);
}
int main(){
	n=read();
	scanf("%s",s+1);
	fr(i,1,n) if(s[i]=='1') ck[i]=1;
	fr(i,2,n){
		ll u=read(),v=read();
		vec[u].push_back(v);
		vec[v].push_back(u);
	}
	dfs0(1);
	cut(1);
//	pf("-----------------\n");
//	print(1);
	fr(k,1,n){
		dfs1(1,k);
		writeln(min(dp[1][0],dp[1][1]));
		if(dp[1][0]<=dp[1][1]) dfs2(1,0,k);
		else dfs2(1,1,k);
		fr(i,1,top){
			ll u=st[i],nxt;
			for(ll v=son[u];v;v=nxt){
				nxt=suf[v];
				del(u,v);
				ins(fa[u],v);
				w[v]+=w[u]+siz[u];
			}
			siz[fa[u]]+=siz[u]+w[u];
			ck[fa[u]]|=ck[u];
			del(fa[u],u);
		}
		top=0;
		cut(1);
//		pf("-----------------\n");
//		print(1);
	}
}