// Original C++ solution (slower):
/*                         _

                        _ooOoo_

                       o8888888o

                       88" . "88

                       (| -_- |)

                       O\  =  /O

                    ____/`---'\____

                  .'  \\|     |//  `.

                 /  \\|||  :  |||//  \

                /  _||||| -:- |||||_  \

                |   | \\\  -  /'| |   |

                | \_|  `\`---'//  |_/ |

                \  .-\__ `-. -'__/-.  /

              ___`. .'  /--.--\  `. .'___

           ."" '<  `.___\_<|>_/___.' _> \"".

          | | :  `- \`. ;`. _/; .'/ /  .' ; |

          \  \ `-.   \_\_`. _.'_/_/  -' _.' /

===========`-.`___`-.__\ \___  /__.-'_.'_.-'================



                  Please give me AC.

*/



#include <iostream>

#include <iomanip>

#include <cstdio>

#include <cmath>

#include <cstdlib>

#include <cstring>

#include <algorithm>

#include <numeric>

#include <string>

#include <sstream>

#include <complex>

#include <bitset>

#include <vector>

#include <list>

#include <set>

#include <map>

#include <queue>

#include <deque>

#include <stack>

#include <unordered_map>

#include <unordered_set>

#include <utility>

#include <chrono>

#include <random>



using namespace std;



using int64 = long long;

using uint64 = unsigned long long;

using vi = vector<int>;

using vl = vector<int64>;

using pii = pair<int, int>;

using pll = pair<int64, int64>;



#define rep(i, n) for (int i = 0; i < (int)(n); ++i)

#define all(v) (v).begin(), (v).end()

#define print(x) cout << (x) << '\n'

#define print2(x, y) cout << (x) << ' ' << (y) << '\n'

#define print3(x, y, z) cout << (x) << ' ' << (y) << ' ' << (z) << '\n'

#define printn(v) rep(i, (v).size() - 1) cout << (v)[i] << ' '; cout << (v)[n - 1] << '\n';

#define debug(x) cerr << #x << ": " << (x) << '\n'

#define debug2(x, y) cerr << #x << ": " << (x) << ", " << #y << ": " << (y) << '\n'

#define debug3(x, y, z) cerr << #x << ": " << (x) << ", " << #y << ": " << (y) << ", " << #z << ": " << (z) << '\n'

#define dbg(v) for (size_t _ = 0; _ < v.size(); ++_){cerr << #v << "[" << _ << "] : " << v[_] << '\n';}

// constant

const int INF = (1 << 30) - 1;

const int64 INF64 = (1LL << 62) - 1;



template<typename T>

T gcd(T a, T b) {

    if (a < b) return gcd(b, a);

    T r;

    while ((r = a % b)) {

        a = b;

        b = r;

    }

    return b;

}



template<typename T>

T lcm(const T a, const T b) {

    return a / gcd(a, b) * b;

}



template<typename T>

bool chmin(T &a, const T &b) {

    if (a > b) return a = b, true; else return false;

}



template<typename T>

bool chmax(T &a, const T &b) {

    if (a < b) return a = b, true; else return false;

}



// End of template.



vector<int> vec[200200];

int a[200200];

int arr[200200];

int ans[200200];



void dfs(int i, int p) {

    const auto it = lower_bound(begin(arr), end(arr), a[i]);

    int x = it - begin(arr);

    int hist = arr[x];

    arr[x] = a[i];

    ans[i] = lower_bound(begin(arr), end(arr), INF) - begin(arr);

    for (int j : vec[i]) if (j != p) {

        dfs(j, i);

    }

    arr[x] = hist;

}



int main() {

    cout << fixed << setprecision(15);

    ios::sync_with_stdio(false);

    cin.tie(nullptr);

    // cin.read(buf, sizeof buf); // 注意: ./a.out < in か pbp | ./a.out で入力すること



    fill(begin(arr), end(arr), INF);

    int n;

    cin >> n;

    rep(i, n) cin >> a[i];

    rep(i, n - 1) {

        int u, v;

        cin >> u >> v;

        --u, --v;

        vec[u].push_back(v);

        vec[v].push_back(u);

    }



    dfs(0, -1);

    rep(i, n) print(ans[i]);



    return 0;

}




// Optimized solution to the same problem (faster):
/*                         _

                        _ooOoo_

                       o8888888o

                       88" . "88

                       (| -_- |)

                       O\  =  /O

                    ____/`---'\____

                  .'  \\|     |//  `.

                 /  \\|||  :  |||//  \

                /  _||||| -:- |||||_  \

                |   | \\\  -  /'| |   |

                | \_|  `\`---'//  |_/ |

                \  .-\__ `-. -'__/-.  /

              ___`. .'  /--.--\  `. .'___

           ."" '<  `.___\_<|>_/___.' _> \"".

          | | :  `- \`. ;`. _/; .'/ /  .' ; |

          \  \ `-.   \_\_`. _.'_/_/  -' _.' /

===========`-.`___`-.__\ \___  /__.-'_.'_.-'================



                  Please give me AC.

*/



#include <iostream>

#include <iomanip>

#include <cstdio>

#include <cmath>

#include <cstdlib>

#include <cstring>

#include <algorithm>

#include <numeric>

#include <string>

#include <sstream>

#include <complex>

#include <bitset>

#include <vector>

#include <list>

#include <set>

#include <map>

#include <queue>

#include <deque>

#include <stack>

#include <unordered_map>

#include <unordered_set>

#include <utility>

#include <chrono>

#include <random>



using namespace std;



using int64 = long long;

using uint64 = unsigned long long;

using vi = vector<int>;

using vl = vector<int64>;

using pii = pair<int, int>;

using pll = pair<int64, int64>;



#define rep(i, n) for (int i = 0; i < (int)(n); ++i)

#define all(v) (v).begin(), (v).end()

#define print(x) cout << (x) << '\n'

#define print2(x, y) cout << (x) << ' ' << (y) << '\n'

#define print3(x, y, z) cout << (x) << ' ' << (y) << ' ' << (z) << '\n'

#define printn(v) rep(i, (v).size() - 1) cout << (v)[i] << ' '; cout << (v)[n - 1] << '\n';

#define debug(x) cerr << #x << ": " << (x) << '\n'

#define debug2(x, y) cerr << #x << ": " << (x) << ", " << #y << ": " << (y) << '\n'

#define debug3(x, y, z) cerr << #x << ": " << (x) << ", " << #y << ": " << (y) << ", " << #z << ": " << (z) << '\n'

#define dbg(v) for (size_t _ = 0; _ < v.size(); ++_){cerr << #v << "[" << _ << "] : " << v[_] << '\n';}

// constant

const int INF = (1 << 30) - 1;

const int64 INF64 = (1LL << 62) - 1;



template<typename T>

T gcd(T a, T b) {

    if (a < b) return gcd(b, a);

    T r;

    while ((r = a % b)) {

        a = b;

        b = r;

    }

    return b;

}



template<typename T>

T lcm(const T a, const T b) {

    return a / gcd(a, b) * b;

}



template<typename T>

bool chmin(T &a, const T &b) {

    if (a > b) return a = b, true; else return false;

}



template<typename T>

bool chmax(T &a, const T &b) {

    if (a < b) return a = b, true; else return false;

}



// End of template.

// begin fast io



char buf[10000000], OUT[10000000];

int bufi = 0, outi = 0;



template<typename T>

void readui(T &n) {

    n = 0;

    int c = buf[bufi++];

    for (; '0' <= c && c <= '9'; c = buf[bufi++])

        n = 10 * n + c - '0';

}



template<typename T>

void readi(T &n) {

    bool negative = false;

    if (buf[bufi] == '-') negative = true, bufi++;

    readui(n);

    if (negative) n = -n;

}



template<typename T>

void readuf(T &x) {

    x = 0;

    T y = 0;

    int z = 0;

    int c = buf[bufi++];

    for (; '0' <= c && c <= '9'; c = buf[bufi++])

        x = 10 * x + c - '0';

    if (buf[bufi - 1] == '.')

        for (; '0' <= c && c <= '9'; c = buf[bufi++], ++z)

            y = 10 * y + c - '0';

    x += y / pow(10, z);

}



template<typename T>

void readf(T &x) {

    bool negative = false;

    if (buf[bufi] == '-') negative = true, bufi++;

    readuf(x);

    if (negative) x = -x;

}



void reads(string &s) {

    const int begin = bufi;

    int c;

    while (c = buf[bufi++], c != ' ' && c != '\n') {}

    s = string(buf + begin, buf + bufi);

}



void readline(string &s) {

    const int begin = bufi;

    while (buf[bufi++] != '\n') {}

    s = string(buf + begin, buf + bufi);

}



const char digit_pairs[] = {

        "00010203040506070809"

        "10111213141516171819"

        "20212223242526272829"

        "30313233343536373839"

        "40414243444546474849"

        "50515253545556575859"

        "60616263646566676869"

        "70717273747576777879"

        "80818283848586878889"

        "90919293949596979899"

};



template<typename T>

void writeui(T n) {

    if (n == 0) OUT[outi++] = '0';

    int size;

    if (n >= 1e12) {

        if (n >= 1e16) {

            if (n >= 1e18) {

                if (n >= 1e19) size = 20;

                else size = 19;

            } else {

                if (n >= 1e17) size = 18;

                else size = 17;

            }

        } else {

            if (n >= 1e14) {

                if (n >= 1e15) size = 16;

                else size = 15;

            } else {

                if (n >= 1e13) size = 14;

                else size = 13;

            }

        }

    } else if (n >= 1e4) {

        if (n >= 1e8) {

            if (n >= 1e10) {

                if (n >= 1e11) size = 12;

                else size = 11;

            } else {

                if (n >= 1e9) size = 10;

                else size = 9;

            }

        } else {

            if (n >= 1e6) {

                if (n >= 1e7) size = 8;

                else size = 7;

            } else {

                if (n >= 1e5) size = 6;

                else size = 5;

            }

        }

    } else {

        if (n >= 1e2) {

            if (n >= 1e3) size = 4;

            else size = 3;

        } else {

            if (n >= 1e1) size = 2;

            else size = 1;

        }

    }

    char *c = OUT + outi + size;

    outi += size;

    while (n >= 100) {

        int x = n % 100;

        n /= 100;

        *--c = digit_pairs[2 * x + 1];

        *--c = digit_pairs[2 * x];

    }

    while (n > 0) {

        *--c = '0' + (n % 10);

        n /= 10;

    }

}





// end fast io





/*

 * Array of linked list. N is max size of array. M is max total size of linked list.

 * An instance must be global variable to zero fill arrays.

*/

template<typename T, int N, int M>

class List {

    int k = 0;

public:

    int head[N];

    pair<int, T> nodes[M];



    class ListNode {

        List<T, N, M> &list;

        int i;

        int pointer;

    public:

        ListNode(List<T, N, M> &list, int i, int pointer = -1) : list(list) {

            this->i = i, this->pointer = pointer;

        }



        void push_back(T x) {

            list.nodes[++list.k].first = list.head[i];

            list.head[i] = list.k;

            list.nodes[list.k].second = x;

        }



        T &operator*() { return list.nodes[pointer].second; }



        bool operator==(ListNode &other) { return pointer == other.pointer; }



        bool operator!=(ListNode &other) { return !pointer == other.pointer; }



        void operator++() { pointer = list.nodes[pointer].first; }



        ListNode begin() {

            return ListNode(list, i, list.head[i]);

        }



        ListNode end() {

            return ListNode(list, i, 0);

        }

    };



    ListNode operator[](int i) {

        return ListNode(*this, i, head[i]);

    }

};



int depth = 0;

List<int, 200100, 400200> vec;

int a[200200];

int arr[200200];

int ans[200200];



void dfs(int i, int p) {

    ++depth;

    const auto it = lower_bound(begin(arr), begin(arr) + depth, a[i]);

    int x = it - begin(arr);

    int hist = arr[x];

    arr[x] = a[i];

    ans[i] = lower_bound(begin(arr) + x, begin(arr) + depth, INF) - begin(arr);

    for (int j : vec[i]) {

        if (j != p) {

            dfs(j, i);

        }

    }

    arr[x] = hist;

    --depth;

}



int main() {

    ios::sync_with_stdio(false);

    cin.tie(nullptr);

    cin.read(buf, sizeof buf); // 注意: ./a.out < in か pbp | ./a.out で入力すること



    fill(begin(arr), end(arr), INF);

    int n;

    readui(n);

    rep(i, n) readui(a[i]);

    rep(i, n - 1) {

        int u, v;

        readui(u), readui(v);

        --u, --v;

        vec[u].push_back(v);

        vec[v].push_back(u);

    }



    dfs(0, -1);

    rep(i, n) writeui(ans[i]), OUT[outi++] = '\n';



    cout.write(OUT, outi);



    return 0;

}




// Fastest known solution for this problem: