You are given a rooted undirected tree consisting of n vertices. Vertex 1 is the root.

Let's denote a depth array of vertex x as an infinite sequence [d_{x, 0}, d_{x, 1}, d_{x, 2}, ...], where d_{x, i} is the number of vertices y such that both conditions hold:

  * x is an ancestor of y; 
  * the simple path from x to y traverses exactly i edges. 



The dominant index of a depth array of vertex x (or, shortly, the dominant index of vertex x) is an index j such that:

  * for every k < j, d_{x, k} < d_{x, j}; 
  * for every k > j, d_{x, k} ≤ d_{x, j}. 



For every vertex in the tree calculate its dominant index.

Input

The first line contains one integer n (1 ≤ n ≤ 10^6) — the number of vertices in a tree.

Then n - 1 lines follow, each containing two integers x and y (1 ≤ x, y ≤ n, x ≠ y). This line denotes an edge of the tree.

It is guaranteed that these edges form a tree.

Output

Output n numbers. i-th number should be equal to the dominant index of vertex i.

Examples

Input

4
1 2
2 3
3 4


Output

0
0
0
0


Input

4
1 2
1 3
1 4


Output

1
0
0
0


Input

4
1 2
2 3
2 4


Output

2
1
0
0
#include <bits/stdc++.h>
using namespace std;
int read() {
  int x = 0;
  char ch = getchar();
  while (!isdigit(ch)) ch = getchar();
  while (isdigit(ch)) x = (x << 1) + (x << 3) + (ch ^ '0'), ch = getchar();
  return x;
}
void print(int x) {
  if (x > 9) print(x / 10);
  putchar(x % 10 + '0');
}
int n, l[1000004], len[1000004], ans[1000004];
vector<int> g[1000004], f[1000004];
void dfs(int x, int par) {
  for (int i = 0; i < g[x].size(); i++) {
    int to = g[x][i];
    if (to != par) {
      dfs(to, x);
      if (len[to] + 1 > len[x]) l[x] = to, len[x] = len[to] + 1;
    }
  }
}
void dfs1(int x, int par) {
  if (!l[x])
    f[x].push_back(1), ans[x] = 0;
  else {
    dfs1(l[x], x);
    swap(f[x], f[l[x]]);
    f[x].push_back(1);
    ans[x] = ans[l[x]];
    if (f[x][ans[x]] == 1) ans[x] = len[x];
    for (int i = 0; i < g[x].size(); i++) {
      int to = g[x][i];
      if (to != par && to != l[x]) {
        dfs1(to, x);
        for (int j = 0; j <= len[to]; j++) {
          f[x][j + len[x] - len[to] - 1] += f[to][j];
          if (f[x][j + len[x] - len[to] - 1] > f[x][ans[x]] ||
              (f[x][j + len[x] - len[to] - 1] == f[x][ans[x]] &&
               ans[x] < j + len[x] - len[to] - 1))
            ans[x] = j + len[x] - len[to] - 1;
        }
      }
    }
  }
}
int main() {
  n = read();
  for (int i = 1; i < n; i++) {
    int u, v;
    u = read(), v = read();
    g[u].push_back(v), g[v].push_back(u);
  }
  dfs(1, -1);
  dfs1(1, -1);
  for (int i = 1; i <= n; i++) print(len[i] - ans[i]), puts("");
}
