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

E. Dasha and Puzzle

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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 u_i, v_i (1 ≤ u_i, v_i ≤ n) that mean that the i-th edge of the tree connects vertices u_i and v_i.

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 x_i, y_i (|x_i|, |y_i| ≤ 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:

-凡-尘

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

E. Dasha and Puzzle

time limit per test：2 seconds

memory limit per test：256 megabytes

input：standard input

output：standard output

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.

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:

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

思路：

如果存在某点度数大于4肯定不行。

然后，第一层让边长为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。即缩小距离的方法。。（摘）

#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <string>
#include <stack>
#include <queue>
#include <vector>
#define inf 0x3f3f3f3f
#define met(a,b) memset(a,b,sizeof a)
#define pb push_back
using namespace std;
typedef long long ll;
const int N = 35;
const int M = 1e5+10;
int n,m,k;
int in[N];
int d[4][2]={{0,1},{1,0},{-1,0},{0,-1}};
vector<int>edg[N];
ll x[N],y[N];
void dfs(int u,int fa,ll xx,ll yy,ll dis,int dir){
    int j=0;
    x[u]=xx;y[u]=yy;
    for(int i=0;i<edg[u].size();i++){
        int v=edg[u][i];
        if(v==fa)continue;
        if(j+dir==3)j++;
        dfs(v,u,xx+d[j][0]*dis,yy+d[j][1]*dis,dis/2,j);
        j++;
    }
}
int main(){
    int u,v;
    bool ok=true;
    scanf("%d",&n);
    for(int i=1;i<n;i++){
        scanf("%d%d",&u,&v);
        edg[u].pb(v);
        edg[v].pb(u);
        in[v]++;in[u]++;
    }
    for(int i=1;i<=n;i++){
        if(in[i]>4){
            ok=false;
            break;
        }
    }
    if(!ok)puts("NO");
    else {
        puts("YES");
        dfs(1,0,0,0,1<<30,-1);
        for(int i=1;i<=n;i++){
            printf("%lld %lld\n",x[i],y[i]);
        }
    }
    return 0;
}