Problem:
Score : 800 points

Problem Statement

We have a tree with N vertices. The vertices are numbered 1, 2, ..., N. The i-th (1 ≦ i ≦ N - 1) edge connects the two vertices A_i and B_i.

Takahashi wrote integers into K of the vertices. Specifically, for each 1 ≦ j ≦ K, he wrote the integer P_j into vertex V_j. The remaining vertices are left empty. After that, he got tired and fell asleep.

Then, Aoki appeared. He is trying to surprise Takahashi by writing integers into all empty vertices so that the following condition is satisfied:

Condition: For any two vertices directly connected by an edge, the integers written into these vertices differ by exactly 1.

Determine if it is possible to write integers into all empty vertices so that the condition is satisfied. If the answer is positive, find one specific way to satisfy the condition.

Constraints

1 ≦ N ≦ 10^5

1 ≦ K ≦ N

1 ≦ A_i, B_i ≦ N (1 ≦ i ≦ N - 1)

1 ≦ V_j ≦ N (1 ≦ j ≦ K) (21:18, a mistake in this constraint was corrected)

0 ≦ P_j ≦ 10^5 (1 ≦ j ≦ K)

The given graph is a tree.

All v_j are distinct.

Input

The input is given from Standard Input in the following format:

N
A_1 B_1
A_2 B_2
:
A_{N-1} B_{N-1}
K
V_1 P_1
V_2 P_2
:
V_K P_K

Output

If it is possible to write integers into all empty vertices so that the condition is satisfied, print Yes. Otherwise, print No.

If it is possible to satisfy the condition, print N lines in addition. The v-th (1 ≦ v ≦ N) of these N lines should contain the integer that should be written into vertex v. If there are multiple ways to satisfy the condition, any of those is accepted.

Sample Input 1

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

Sample Output 1

Yes
5
6
6
5
7

The figure below shows the tree when Takahashi fell asleep. For each vertex, the integer written beside it represents the index of the vertex, and the integer written into the vertex is the integer written by Takahashi.

Aoki can, for example, satisfy the condition by writing integers into the remaining vertices as follows:

This corresponds to Sample Output 1. Note that other outputs that satisfy the condition will also be accepted, such as:

Yes
7
6
8
7
7

Sample Input 2

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

Sample Output 2

No

Sample Input 3

4
1 2
2 3
3 4
1
1 0

Sample Output 3

Yes
0
-1
-2
-3

The integers written by Aoki may be negative or exceed 10^6.

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

// eddy1021
#include <bits/stdc++.h>
using namespace std;
typedef double D;
typedef long double LD;
typedef long long ll;
typedef long long LL;
typedef pair<int,int> PII;
typedef pair<LL,LL> PLL;
typedef pair<LD,LD> Pt;
typedef tuple<int,int,int> tiii;
typedef tuple<LL,LL,LL> tlll;
#define mod9 1000000009ll
#define mod7 1000000007ll
#define INF  1023456789ll
#define INF16 10000000000000000ll
#define FI first
#define SE second
#define X FI
#define Y SE
#define PB push_back
#define MP make_pair
#define MT make_tuple
#define eps 1e-9
#define SZ(x) (int)(x).size()
#define ALL(x) (x).begin(), (x).end()
#ifndef ONLINE_JUDGE
#define debug(...) printf(__VA_ARGS__)
#else 
#define debug(...)
#endif
inline LL getint(){
  LL _x=0,_tmp=1; char _tc=getchar();    
  while( (_tc<'0'||_tc>'9')&&_tc!='-' ) _tc=getchar();
  if( _tc == '-' ) _tc=getchar() , _tmp = -1;
  while(_tc>='0'&&_tc<='9') _x*=10,_x+=(_tc-'0'),_tc=getchar();
  return _x*_tmp;
}
inline LL add( LL _x , LL _y , LL _mod = mod7 ){
  _x += _y;
  return _x >= _mod ? _x - _mod : _x;
}
inline LL sub( LL _x , LL _y , LL _mod = mod7 ){
  _x -= _y;
  return _x < 0 ? _x + _mod : _x;
}
inline LL mul( LL _x , LL _y , LL _mod = mod7 ){
  _x *= _y;
  return _x >= _mod ? _x % _mod : _x;
}
LL mypow( LL _a , LL _x , LL _mod ){
  if( _x == 0 ) return 1LL;
  LL _ret = mypow( mul( _a , _a , _mod ) , _x >> 1 , _mod );
  if( _x & 1 ) _ret = mul( _ret , _a , _mod );
  return _ret;
}
LL mymul( LL _a , LL _x , LL _mod ){
  if( _x == 0 ) return 0LL;
  LL _ret = mymul( add( _a , _a , _mod ) , _x >> 1 , _mod );
  if( _x & 1 ) _ret = add( _ret , _a , _mod );
  return _ret;
}
inline bool equal( D _x ,  D _y ){
  return _x > _y - eps && _x < _y + eps;
}
int __ = 1 , _cs;
/*********default*********/
#define N 101010
void build(){

}
vector< int > v[ N ];
int n , q , clr[ N ];
bool st[ N ];
void init(){
  n = getint();
  for( int i = 1 ; i < n ; i ++ ){
    int ai = getint();
    int bi = getint();
    v[ ai ].push_back( bi );
    v[ bi ].push_back( ai );
  }
  q = getint(); while( q -- ){
    int vi = getint();
    int pi = getint();
    st[ vi ] = true;
    clr[ vi ] = pi;
  }
}
int type[ 2 ] , odd[ N ];
inline bool okay( int now , int prt , int dep ){
  if( st[ now ] ){
    if( type[ dep ] && type[ dep ] - 1 != clr[ now ] % 2 )
      return false;
    type[ dep ] = clr[ now ] % 2 + 1;
  }
  for( int son : v[ now ] ){
    if( son == prt ) continue;
    if( !okay( son , now , 1 - dep ) )
      return false;
  }
  return true;
}
int lb[ N ] , rb[ N ];
bool got[ N ];
void gogo(){
  priority_queue< PII , vector<PII> , greater<PII> > heap;
  for( int i = 1 ; i <= n ; i ++ )
    if( !st[ i ] )
      heap.push( { rb[ i ] - lb[ i ] , i } );
  while( heap.size() ){
    PII tp = heap.top(); heap.pop();
    int who = tp.second;
    if( st[ who ] ) continue;
    for( int x : v[ who ] )
      if( st[ x ] ){
        lb[ who ] = max( lb[ who ] , lb[ x ] - 1 );
        rb[ who ] = min( rb[ who ] , rb[ x ] + 1 );
      }
    if( lb[ who ] > rb[ who ] ){
      puts( "No" );
      exit( 0 );
    }
    st[ who ] = true;
    clr[ who ] = lb[ who ];
  }
}
void solve(){
  if( !okay( 1 , 1 , 0 ) ){
    puts( "No" );
    exit( 0 );
  }
  queue< int > Q;
  for( int i = 1 ; i <= n ; i ++ )
    if( st[ i ] ){
      got[ i ] = true;
      Q.push( i );
      lb[ i ] = rb[ i ] = clr[ i ];
    }
  while( Q.size() ){
    int tn = Q.front(); Q.pop();
    for( int son : v[ tn ] ){
      if( got[ son ] ){
        lb[ son ] = max( lb[ son ] , lb[ tn ] - 1 );
        rb[ son ] = min( rb[ son ] , rb[ tn ] + 1 );
      }else{
        got[ son ] = true;
        Q.push( son );
        lb[ son ] = lb[ tn ] - 1;
        rb[ son ] = rb[ tn ] + 1;
      }
    }
  }
  for( int i = 1 ; i <= n ; i ++ )
    if( lb[ i ] > rb[ i ] ){
      puts( "No" );
      exit( 0 );
    }
  gogo();
  if( !okay( 1 , 1 , 0 ) ){
    puts( "No" );
    exit( 0 );
  }
  puts( "Yes" );
  for( int i = 1 ; i <= n ; i ++ )
    printf( "%d\n" , clr[ i ] );
}
int main(){
  build();
  //__ = getint();
  while( __ -- ){
    init();
    solve();
  }
}