Codeforces Round #394 (Div. 2) E. Dasha and Puzzle 构造

E. Dasha and Puzzle

题目连接：

http://codeforces.com/contest/761/problem/E

Description

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.

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.

Sample Input

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

Sample Output

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

Hint

题意

给你一棵树，让你在二维平面上摆出来，边必须平行坐标轴，且边没有交集。

题解：

如果存在某点度数大于4肯定不行。

然后我们脑补一下，第一层我让边长为len，第二层边长为len/2，第三层边长为len/4……

这样弄下去就好了，这样就保证每一层都不会碰到上一层了。

有些细节，这个稍微抠一下就好了。

代码

#include<bits/stdc++.h>
using namespace std;
const int maxn = 10005;
vector<int> E[maxn];
int n;
long long X[maxn],Y[maxn];
int dx[5]={1,-1,0,0,0};
int dy[5]={0,0,1,-1,0};
void dfs(int x,int f,long long len,int dir,long long lx,long long ly){
    X[x]=len*dx[dir]+lx;
    Y[x]=len*dy[dir]+ly;
    int ndir = -1;
    if(dir==0)ndir=1;
    else if(dir==1)ndir=0;
    else if(dir==2)ndir=3;
    else if(dir==3)ndir=2;
    vector<int>op;
    for(int i=0;i<4;i++)
        if(i!=ndir)op.push_back(i);
    int st=0;
    for(int i=0;i<E[x].size();i++){
        int v = E[x][i];
        if(v==f)continue;
        dfs(v,x,len/2-1,op[st++],X[x],Y[x]);
    }
}
int main(){
    scanf("%d",&n);
    for(int i=0;i<n-1;i++){
        int a,b;

        scanf("%d%d",&a,&b);
        a--,b--;
        E[a].push_back(b);
        E[b].push_back(a);
    }
    for(int i=0;i<n;i++){
        if(E[i].size()>4){
            cout<<"NO"<<endl;
            return 0;
        }
    }
    dfs(0,-1,1e16,4,0,0);
    cout<<"YES"<<endl;
    for(int i=0;i<n;i++)
        cout<<X[i]<<" "<<Y[i]<<endl;
}