// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;

fn main() {
    input! {
        n: usize,
        a: [i64; n],
        uv: [(Usize1,Usize1); n-1],
    }
    let mut tree = vec![vec![]; n];
    for (u, v) in uv {
        tree[u].push(v);
        tree[v].push(u);
    }

    let mut res = vec![0; n];
    res[0] = 1;
    dfs(&tree, &a, &mut vec![1_000_000_000_000], &mut res, 0, 0);
    for x in res {
        println!("{}", x);
    }
}

fn dfs(
    tree: &Vec<Vec<usize>>,
    a: &Vec<i64>,
    l: &mut Vec<i64>,
    res: &mut Vec<usize>,
    v: usize,
    p: usize,
) {
    let mut f = None;
    if matches!(l.last(), Some(x) if *x < a[v]) {
        l.push(a[v]);
    } else {
        let i = kyopro_lib::misc::lower_bound(0, l.len(), |i| l[i] >= a[v]);
        f = Some((i, l[i]));
        l[i] = a[v];
    }
    res[v] = l.len();

    for &u in &tree[v] {
        if u == p {
            continue;
        }
        dfs(tree, a, l, res, u, v);
    }
    if let Some((i, x)) = f {
        l[i] = x;
    } else {
        l.pop();
    }
}
*/

fn main() {
    let exe = "/tmp/bin5BC23C59";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "
f0VMRgIBAQAAAAAAAAAAAAIAPgABAAAAYANAAAAAAABAAAAAAAAAAHCCAwAAAAAAAAAAAEAAOAAHAEAA
EAAPAAEAAAAFAAAAAAAAAAAAAAAAAEAAAAAAAAAAQAAAAAAAqGcDAAAAAACoZwMAAAAAAAAAIAAAAAAA
AQAAAAYAAAAgagMAAAAAACBqYwAAAAAAIGpjAAAAAAC4FwAAAAAAAAgzAAAAAAAAAAAgAAAAAAAEAAAA
BAAAAMgBAAAAAAAAyAFAAAAAAADIAUAAAAAAACQAAAAAAAAAJAAAAAAAAAAEAAAAAAAAAAcAAAAEAAAA
IGoDAAAAAAAgamMAAAAAACBqYwAAAAAAMAAAAAAAAADIAAAAAAAAACAAAAAAAAAAUOV0ZAQAAAAsIgMA
AAAAACwiQwAAAAAALCJDAAAAAADcCQAAAAAAANwJAAAAAAAABAAAAAAAAABR5XRkBgAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQAAAAAAAAAFLldGQEAAAAIGoDAAAAAAAgamMA
AAAAACBqYwAAAAAA4BUAAAAAAADgFQAAAAAAAAEAAAAAAAAABAAAABQAAAADAAAAR05VAKxvCBjscYZ1
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AAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAAB4AAAABAAAABgAAAAAAAADsAUAAAAAAAOwBAAAAAAAA
AwAAAAAAAAAAAAAAAAAAAAEAAAAAAAAAAAAAAAAAAAAkAAAAAQAAAAYAAAAAAAAA8AFAAAAAAADwAQAA
AAAAAJa7AgAAAAAAAAAAAAAAAAAQAAAAAAAAAAAAAAAAAAAAKgAAAAEAAAAGAAAAAAAAAIa9QgAAAAAA
hr0CAAAAAAADAAAAAAAAAAAAAAAAAAAAAQAAAAAAAAAAAAAAAAAAADAAAAABAAAAAgAAAAAAAACgvUIA
AAAAAKC9AgAAAAAAi2QAAAAAAAAAAAAAAAAAACAAAAAAAAAAAAAAAAAAAAA4AAAAAQAAAAIAAAAAAAAA
LCJDAAAAAAAsIgMAAAAAANwJAAAAAAAAAAAAAAAAAAAEAAAAAAAAAAAAAAAAAAAARgAAAAEAAHACAAAA
AAAAAAgsQwAAAAAACCwDAAAAAACgOwAAAAAAAAAAAAAAAAAACAAAAAAAAAAAAAAAAAAAAFAAAAABAAAA
AwQAAAAAAAAgamMAAAAAACBqAwAAAAAAMAAAAAAAAAAAAAAAAAAAACAAAAAAAAAAAAAAAAAAAABXAAAA
CAAAAAMEAAAAAAAAYGpjAAAAAABQagMAAAAAAIgAAAAAAAAAAAAAAAAAAAAgAAAAAAAAAAAAAAAAAAAA
XQAAAAEAAAADAAAAAAAAAGBqYwAAAAAAYGoDAAAAAADQEwAAAAAAAAAAAAAAAAAAIAAAAAAAAAAAAAAA
AAAAAGoAAAABAAAAAwAAAAAAAAAwfmMAAAAAADB+AwAAAAAAuAEAAAAAAAAAAAAAAAAAAAgAAAAAAAAA
CAAAAAAAAABvAAAAAQAAAAMAAAAAAAAAAIBjAAAAAAAAgAMAAAAAANgBAAAAAAAAAAAAAAAAAAAgAAAA
AAAAAAAAAAAAAAAAdQAAAAgAAAADAAAAAAAAAOCBYwAAAAAA2IEDAAAAAABIGwAAAAAAAAAAAAAAAAAA
IAAAAAAAAAAAAAAAAAAAAHoAAAABAAAAMAAAAAAAAAAAAAAAAAAAANiBAwAAAAAAEQAAAAAAAAAAAAAA
AAAAAAEAAAAAAAAAAQAAAAAAAAABAAAAAwAAAAAAAAAAAAAAAAAAAAAAAADpgQMAAAAAAIMAAAAAAAAA
AAAAAAAAAAABAAAAAAAAAAAAAAAAAAAA
";


Measured memory_bytes: 39132