#[allow(dead_code)]
fn is_whitespace(c: &char) -> bool {
    c.is_whitespace()
}

#[allow(dead_code)]
fn is_eol(c: &char) -> bool {
    ['\r', '\n'].contains(c)
}

#[allow(unused_macros)]
macro_rules! input {
    ($var:ident, $($r:tt)*) => {
        input_inner!{$var, $($r)*}
    };

    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        #[allow(unused_mut, unused_variables, bare_trait_objects)]
        let mut next = move |f: &Fn(&char)->bool| -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|f(&c))
                .take_while(|c|!f(&c))
                .collect()
        };
        input_inner!{next, $($r)*};
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; eol ]) => {
        $next(&is_eol).split(' ').map(|x| x.parse::<$t>().unwrap()).collect::<Vec<_>>()
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, parser) => {
        $next
    };

    ($next:expr, $t:ty) => {
        $next(&is_whitespace).parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{BinaryHeap, HashMap, HashSet};

#[allow(dead_code)]
struct Edge {
    from: usize,
    to: usize,
}

#[allow(dead_code)]
type Graph = Vec<Vec<usize>>;
#[allow(dead_code)]
const M: usize = 1_000_000_007;

use std::cmp::Ordering;
trait BinarySearch<T> {
    fn upper_bound(&self, value: &T) -> Option<usize>;
    fn lower_bound(&self, value: &T) -> Option<usize>;
}

impl<T: Ord> BinarySearch<T> for [T] {
    fn upper_bound(&self, value: &T) -> Option<usize> {
        let (mut ng, mut ok) = (-1, self.len() as isize);
        while (ok - ng).abs() > 1 {
            let mid = ((ok + ng) / 2) as usize;
            match value.cmp(&self[mid]) {
                Ordering::Less => {
                    ok = mid as isize;
                }
                Ordering::Equal | Ordering::Greater => {
                    ng = mid as isize;
                }
            };
        }
        if ok >= 0 && ok < self.len() as isize {
            Some(ok as usize)
        } else {
            None
        }
    }

    fn lower_bound(&self, value: &T) -> Option<usize> {
        let (mut ng, mut ok) = (-1, self.len() as isize);
        while (ok - ng).abs() > 1 {
            let mid = ((ok + ng) / 2) as usize;
            match value.cmp(&self[mid]) {
                Ordering::Less | Ordering::Equal => {
                    ok = mid as isize;
                }
                Ordering::Greater => {
                    ng = mid as isize;
                }
            };
        }
        if ok >= 0 && ok < self.len() as isize {
            Some(ok as usize)
        } else {
            None
        }
    }
}

fn dfs(
    par: usize,
    pos: usize,
    lis: &mut Vec<usize>,
    graph: &Vec<Vec<usize>>,
    a: &Vec<usize>,
    ans: &mut Vec<usize>,
) {
    let res = lis.lower_bound(&a[pos]);
    let mut old = None;
    if let Some(index) = res {
        old = Some(lis[index]);
        lis[index] = a[pos];
    } else {
        lis.push(a[pos]);
    }
    ans[pos] = lis.len();
    for &next in &graph[pos] {
        if par == next {
            continue;
        }
        dfs(pos, next, lis, graph, a, ans);
    }
    if let Some(v) = old {
        let idx = lis.lower_bound(&a[pos]);
        lis[idx.unwrap()] = v;
    } else {
        lis.pop();
    }
}

fn main() {
    input! {
        n: usize,
        a: [usize; n],
        edges: [(usize1, usize1); n-1],
    }
    let mut graph = vec![vec![]; n];
    for &(f, t) in &edges {
        graph[f].push(t);
        graph[t].push(f);
    }
    let mut ans = vec![0; n];
    let mut lis = vec![];
    dfs(0, 0, &mut lis, &graph, &a, &mut ans);
    for x in ans {
        println!("{}", x);
    }
}


Measured memory_bytes: 39268