// writer: w33z8kqrqk8zzzx33
#include <bits/stdc++.h>
using namespace std;

// begin fast read template by CYJian (source: https://www.luogu.com.cn/paste/i11c3ppx)

namespace io {
	const int __SIZE = (1 << 21) + 1;
	char ibuf[__SIZE], *iS, *iT, obuf[__SIZE], *oS = obuf, *oT = oS + __SIZE - 1, __c, qu[55]; int __f, qr, _eof;
	#define Gc() (iS == iT ? (iT = (iS = ibuf) + fread (ibuf, 1, __SIZE, stdin), (iS == iT ? EOF : *iS ++)) : *iS ++)
	inline void flush () { fwrite (obuf, 1, oS - obuf, stdout), oS = obuf; }
	inline void gc (char &x) { x = Gc(); }
	inline void pc (char x) { *oS ++ = x; if (oS == oT) flush (); }
	inline void pstr (const char *s) { int __len = strlen(s); for (__f = 0; __f < __len; ++__f) pc (s[__f]); }
	inline void gstr (char *s) { for(__c = Gc(); __c < 32 || __c > 126 || __c == ' ';)  __c = Gc();
		for(; __c > 31 && __c < 127 && __c != ' '; ++s, __c = Gc()) *s = __c; *s = 0; }
	template <class I> inline bool gi (I &x) { _eof = 0;
		for (__f = 1, __c = Gc(); (__c < '0' || __c > '9') && !_eof; __c = Gc()) { if (__c == '-') __f = -1; _eof |= __c == EOF; }
		for (x = 0; __c <= '9' && __c >= '0' && !_eof; __c = Gc()) x = x * 10 + (__c & 15), _eof |= __c == EOF; x *= __f; return !_eof; }
	template <class I> inline void print (I x) { if (!x) pc ('0'); if (x < 0) pc ('-'), x = -x;
		while (x) qu[++ qr] = x % 10 + '0',  x /= 10; while (qr) pc (qu[qr --]); }
	struct Flusher_ {~Flusher_(){flush();}}io_flusher_;
} using io::pc; using io::gc; using io::pstr; using io::gstr; using io::gi; using io::print;

// end fast read template by CYJian

#define iter(i, a, b) for(int i=(a); i<(b); i++)
#define rep(i, a) iter(i, 0, a)
#define rep1(i, a) iter(i, 1, (a)+1)
#define log(a) cerr<<"\033[32m[DEBUG] "<<#a<<'='<<(a)<<" @ line "<<__LINE__<<"\033[0m"<<endl
#define all(a) a.begin(), a.end()
#define fi first
#define se second
#define pb push_back
#define mp make_pair
 
using ll=long long;
using pii=pair<int, int>;
//#define int ll
const int MOD = 1000000007;

int a[200005];
vector<int> elist[200005];

class SST {
public:
	int dep, mx;
	stack<int> mxp;
	SST* ch[2];
	SST(int dep) : dep(dep), mx(0), mxp() {
		ch[0] = nullptr;
		ch[1] = nullptr;
	}
	~SST() {
		if(ch[0]) delete ch[0];
		if(ch[1]) delete ch[1];
	}
	void inc(int val, int diff) {
		mxp.push(mx);
		mx = max(mx, diff);
		if (!dep)
			return;
		bool cv = val & (1 << (dep - 1));
		if (!ch[cv])
			ch[cv] = new SST(dep - 1);
		ch[cv]->inc(val, diff);
	}
	void undo(int val) {
		mx = mxp.top();
		mxp.pop();
		if (!dep) return;
		bool cv = val & (1 << (dep - 1));
		ch[cv]->undo(val);
	}
	int psum(int val) {
		if (!dep)
			return mx;
		int ans = 0;
		bool cv = val & (1 << (dep - 1));
		if (ch[cv])
			ans = ch[cv]->psum(val);
		if (cv && ch[0])
			ans = max(ans, ch[0]->mx);
		return ans;
	}
};

int ans[200005];

SST* root;
void dfs(int u, int fa) {
	ans[u] = root->psum(a[u]-1)+1;
	root->inc(a[u], ans[u]);
	for(int& v:elist[u]) if(v != fa) dfs(v, u);
	root->undo(a[u]);
}

void dfs2(int u, int fa) {
	ans[u] = max(ans[u], ans[fa]);
	for(int& v:elist[u]) if(v != fa) dfs2(v, u);
}

int cp[200005];

signed main() {
    ios_base::sync_with_stdio(false); cin.tie(0);
    int n; gi(n);
	rep1(i, n) {
		gi(a[i]);
		cp[i] = a[i];
	}
	sort(cp+1, cp+n+1); int* cu = unique(cp+1, cp+n+1);
	rep1(i, n) a[i] = lower_bound(cp+1, cu, a[i]) - cp;
	rep(i, n-1) {
		int u,v ; gi(u), gi(v);
		elist[u].pb(v); elist[v].pb(u);
	}
	root = new SST(19);
	dfs(1, 0);
	dfs2(1, 0);
	rep1(i, n) print(ans[i]), pc('\n');
}


Measured memory_bytes: 324556