Problem: Dasha decided to have a rest after solving the problem. She had been ready to start her favourite activity — origami, but remembered the puzzle that she could not solve. 

<image>

The tree is a non-oriented connected graph without cycles. In particular, there always are n - 1 edges in a tree with n vertices.

The puzzle is to position the vertices at the points of the Cartesian plane with integral coordinates, so that the segments between the vertices connected by edges are parallel to the coordinate axes. Also, the intersection of segments is allowed only at their ends. Distinct vertices should be placed at different points. 

Help Dasha to find any suitable way to position the tree vertices on the plane.

It is guaranteed that if it is possible to position the tree vertices on the plane without violating the condition which is given above, then you can do it by using points with integral coordinates which don't exceed 1018 in absolute value.

Input

The first line contains single integer n (1 ≤ n ≤ 30) — the number of vertices in the tree. 

Each of next n - 1 lines contains two integers ui, vi (1 ≤ ui, vi ≤ n) that mean that the i-th edge of the tree connects vertices ui and vi.

It is guaranteed that the described graph is a tree.

Output

If the puzzle doesn't have a solution then in the only line print "NO".

Otherwise, the first line should contain "YES". The next n lines should contain the pair of integers xi, yi (|xi|, |yi| ≤ 1018) — the coordinates of the point which corresponds to the i-th vertex of the tree.

If there are several solutions, print any of them. 

Examples

Input

7
1 2
1 3
2 4
2 5
3 6
3 7

Output

YES
0 0
1 0
0 1
2 0
1 -1
-1 1
0 2

Input

6
1 2
2 3
2 4
2 5
2 6


Output

NO


Input

4
1 2
2 3
3 4

Output

YES
3 3
4 3
5 3
6 3

Note

In the first sample one of the possible positions of tree is: <image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#pragma GCC optimize("O3")
using namespace std;
struct custom_hash {
  static uint64_t splitmix64(uint64_t x) {
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
  }
  size_t operator()(uint64_t x) const {
    static const uint64_t FIXED_RANDOM =
        chrono::steady_clock::now().time_since_epoch().count();
    return splitmix64(x + FIXED_RANDOM);
  }
};
template <typename T, size_t N>
int SIZE(const T (&t)[N]) {
  return N;
}
template <typename T>
int SIZE(const T &t) {
  return t.size();
}
string to_string(const string s, int x1 = 0, int x2 = 1e9) {
  return '"' + ((x1 < s.size()) ? s.substr(x1, x2 - x1 + 1) : "") + '"';
}
string to_string(const char *s) { return to_string((string)s); }
string to_string(const bool b) { return (b ? "true" : "false"); }
string to_string(const char c) { return string({c}); }
template <size_t N>
string to_string(const bitset<N> &b, int x1 = 0, int x2 = 1e9) {
  string t = "";
  for (int __iii__ = min(x1, SIZE(b)), __jjj__ = min(x2, SIZE(b) - 1);
       __iii__ <= __jjj__; ++__iii__) {
    t += b[__iii__] + '0';
  }
  return '"' + t + '"';
}
template <typename A, typename... C>
string to_string(const A(&v), int x1 = 0, int x2 = 1e9, C... coords);
int l_v_l_v_l = 0, t_a_b_s = 0;
template <typename A, typename B>
string to_string(const pair<A, B> &p) {
  l_v_l_v_l++;
  string res = "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
  l_v_l_v_l--;
  return res;
}
template <typename A, typename... C>
string to_string(const A(&v), int x1, int x2, C... coords) {
  int rnk = rank<A>::value;
  string tab(t_a_b_s, ' ');
  string res = "";
  bool first = true;
  if (l_v_l_v_l == 0) res += '\n';
  res += tab + "[";
  x1 = min(x1, SIZE(v)), x2 = min(x2, SIZE(v));
  auto l = begin(v);
  advance(l, x1);
  auto r = l;
  advance(r, (x2 - x1) + (x2 < SIZE(v)));
  for (auto e = l; e != r; e = next(e)) {
    if (!first) {
      res += ", ";
    }
    first = false;
    l_v_l_v_l++;
    if (e != l) {
      if (rnk > 1) {
        res += '\n';
        t_a_b_s = l_v_l_v_l;
      };
    } else {
      t_a_b_s = 0;
    }
    res += to_string(*e, coords...);
    l_v_l_v_l--;
  }
  res += "]";
  if (l_v_l_v_l == 0) res += '\n';
  return res;
}
void dbgm() { ; }
template <typename Heads, typename... Tails>
void dbgm(Heads H, Tails... T) {
  cout << to_string(H) << " | ";
  dbgm(T...);
}
const long long MOD = (int)1e9 + 7;
const long long INF = 2e18 + 5;
struct hashLL {
  size_t operator()(long long x) const {
    x = (x ^ (x >> 30)) * UINT64_C(0xbf58476d1ce4e5b9);
    x = (x ^ (x >> 27)) * UINT64_C(0x94d049bb133111eb);
    x = x ^ (x >> 31);
    return x;
  }
};
long long inv(long long a, long long b) {
  return 1 < a ? b - inv(b % a, a) * b / a : 1;
}
long long gcd(long long a, long long b, long long &x, long long &y) {
  if (a == 0) {
    x = 0;
    y = 1;
    return b;
  }
  long long x1, y1;
  long long d = gcd(b % a, a, x1, y1);
  x = y1 - (b / a) * x1;
  y = x1;
  return d;
}
long long distsq(long long x1, long long y1, long long x2, long long y2) {
  return (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1);
}
const int N = 31;
long long n, m;
long long lt[N];
long long rt[N];
long long up[N];
long long dn[N];
long long degree[N];
long long u, v;
vector<int> g[N];
long long xx[N];
long long yy[N];
long long vis[N];
int used[N][4];
int opp[4] = {1, 0, 3, 2};
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n;
  memset(vis, 0, sizeof(vis));
  memset(used, 0, sizeof(used));
  for (int i = 1; i <= (n); i++) {
    lt[i] = dn[i] = -1e18;
    rt[i] = up[i] = 1e18;
  }
  for (int i = 0; i < (n - 1); i++) {
    cin >> u >> v;
    degree[u]++;
    degree[v]++;
    if (degree[u] > 4 || degree[v] > 4) {
      cout << "NO";
      return 0;
    }
    g[u].push_back(v);
    g[v].push_back(u);
  }
  long long fst = 1;
  deque<long long> q;
  q.push_back(fst);
  xx[fst] = yy[fst] = 0;
  while (!q.empty()) {
    auto idx = q.front();
    q.pop_front();
    vis[idx] = 1;
    long long l = lt[idx];
    long long r = rt[idx];
    long long u = up[idx];
    long long d = dn[idx];
    int dir = 0;
    for (auto nei : g[idx]) {
      if (vis[nei]) continue;
      if (used[idx][dir]) dir++;
      used[idx][dir] = 1;
      used[nei][opp[dir]] = 1;
      lt[nei] = l, rt[nei] = r, up[nei] = u, dn[nei] = d;
      if (dir == 0) {
        rt[nei] = xx[idx];
      } else if (dir == 1) {
        lt[nei] = xx[idx];
      } else if (dir == 2) {
        dn[nei] = yy[idx];
      } else if (dir == 3) {
        up[nei] = yy[idx];
      }
      if (dir == 0 || dir == 1) {
        up[nei] = (up[idx] + yy[idx]) / 2;
        dn[nei] = (dn[idx] + yy[idx]) / 2;
      }
      if (dir == 2 || dir == 3) {
        lt[nei] = (lt[idx] + xx[idx]) / 2;
        rt[nei] = (rt[idx] + xx[idx]) / 2;
      }
      xx[nei] = (lt[nei] + rt[nei]) / 2;
      yy[nei] = (up[nei] + dn[nei]) / 2;
      dir++;
      q.push_back(nei);
    }
  }
  cout << "YES\n";
  for (int i = 1; i <= (n); i++) {
    cout << xx[i] << ' ' << yy[i] << '\n';
  }
  return 0;
}