We have a tree with N vertices, whose i-th edge connects Vertex u_i and Vertex v_i. Vertex i has an integer a_i written on it. For every integer k from 1 through N, solve the following problem:

* We will make a sequence by lining up the integers written on the vertices along the shortest path from Vertex 1 to Vertex k, in the order they appear. Find the length of the longest increasing subsequence of this sequence.



Here, the longest increasing subsequence of a sequence A of length L is the subsequence A_{i_1} , A_{i_2} , ... , A_{i_M} with the greatest possible value of M such that 1 \leq i_1 < i_2 < ... < i_M \leq L and A_{i_1} < A_{i_2} < ... < A_{i_M}.

Constraints

* 2 \leq N \leq 2 \times 10^5
* 1 \leq a_i \leq 10^9
* 1 \leq u_i , v_i \leq N
* u_i \neq v_i
* The given graph is a tree.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
a_1 a_2 ... a_N
u_1 v_1
u_2 v_2
:
u_{N-1} v_{N-1}


Output

Print N lines. The k-th line, print the length of the longest increasing subsequence of the sequence obtained from the shortest path from Vertex 1 to Vertex k.

Example

Input

10
1 2 5 3 4 6 7 3 2 4
1 2
2 3
3 4
4 5
3 6
6 7
1 8
8 9
9 10


Output

1
2
3
3
4
4
5
2
2
3
#include<bits/stdc++.h>
using namespace std;
const int N=2e5+5;
struct edge{
	int to,nt;
}e[N<<1];
int ans[N],d[N],a[N],cnt=1,h[N],n;
void add(int u,int v){
	e[cnt]={v,h[u]};
	h[u]=cnt++;
}
void dfs(int u,int fa){
	int p=lower_bound(d+1,d+n+1,a[u])-d;
	int tmp=d[p];
	d[p]=a[u];
	ans[u]=max(ans[fa],p);
	for(int i=h[u];i;i=e[i].nt)
	{
		 int v=e[i].to;
		 if(v==fa) continue;
		 dfs(v,u);
	}
	d[p]=tmp;
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d",&a[i]);
	for(int i=1,u,v;i<n;i++)
	{
		scanf("%d%d",&u,&v);
		add(u,v),add(v,u);
	}
	memset(d,0x3f,sizeof d);
	dfs(1,0);
	for(int i=1;i<=n;i++)
		printf("%d\n",ans[i]);
	return 0;
}