Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/python
import sys
from scipy.sparse import*
g=[]
n=int(sys.stdin.readline())
for _ in xrange(n-1):
	a,b=map(int,sys.stdin.readline().split())
	g.append((a-1,b-1,1))
z=[-1]*n
for _ in xrange(int(sys.stdin.readline())):
	a,b=map(int,sys.stdin.readline().split())
	g.append((n,a-1,b))
	z[a-1]=b
a,b,c=zip(*g)
a=map(int,csgraph.dijkstra(coo_matrix((c,(a,b)),[n+1]*2),0,n))
for i in xrange(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		exit()
for e in g:
	if e[0]<e[1] and abs(a[e[0]]-a[e[1]])!=1:
		print('No')
		exit()
print('Yes')
print("\n".join(map(str,a[:n])))

Fixed submission:
#!/usr/bin/python
def shortestPath(g,s,dist,prev):
	n = len(g)-1
	Q=[]
	heapq.heappush(Q,(0,-2,s))
	while Q:
		e = heapq.heappop(Q)
		if prev[e[2]]!=-1: continue
		prev[e[2]] = e[1]
		for f in g[e[2]]:
			if dist[f[2]] > e[0] + f[0]:
				dist[f[2]] = e[0] + f[0]
				heapq.heappush(Q,(e[0]+f[0],f[1],f[2]))

import sys,heapq
#if sys.version_info[0]>=3:raw_input=input

n=int(raw_input())
g=[[] for _ in range(n+1)]
for _ in xrange(n-1):
	a,b=map(int,raw_input().split())
	g[a-1]+=[(1,a-1,b-1)]
	g[b-1]+=[(1,b-1,a-1)]
z=[-1]*n
for _ in xrange(int(raw_input())):
	a,b=map(int,raw_input().split())
	g[n]+=[(b,n,a-1)]
	z[a-1]=b
a=[1e9]*n+[0]
shortestPath(g,n,a,[-1]*(n+1))
for i in xrange(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		sys.exit()
for _ in g:
	for e in _:
		if e[1]<e[2] and abs(a[e[1]]-a[e[2]])!=1:
			print('No')
			sys.exit()
print('Yes')
print("\n".join(map(str,a[:n])))

Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/python
import sys
from scipy.sparse import*
g=[]
n=int(sys.stdin.readline())
for _ in xrange(n-1):
	a,b=map(int,sys.stdin.readline().split())
	g.append((a-1,b-1,1))
z=[-1]*n
for _ in xrange(int(sys.stdin.readline())):
	a,b=map(int,sys.stdin.readline().split())
	g.append((n,a-1,b))
	z[a-1]=b
a,b,c=zip(*g)
a=map(int,csgraph.dijkstra(csc_matrix((c,(a,b)),[n+1]*2),0,n))
for i in xrange(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		exit()
for e in g:
	if e[0]<e[1] and abs(a[e[0]]-a[e[1]])!=1:
		print('No')
		exit()
print('Yes')
print("\n".join(map(str,a[:n])))

Fixed submission:
#!/usr/bin/python
def shortestPath(g,s,dist,prev):
	n = len(g)-1
	Q=[]
	heapq.heappush(Q,(0,-2,s))
	while Q:
		e = heapq.heappop(Q)
		if prev[e[2]]!=-1: continue
		prev[e[2]] = e[1]
		for f in g[e[2]]:
			if dist[f[2]] > e[0] + f[0]:
				dist[f[2]] = e[0] + f[0]
				heapq.heappush(Q,(e[0]+f[0],f[1],f[2]))

import sys,heapq
#if sys.version_info[0]>=3:raw_input=input

n=int(raw_input())
g=[[] for _ in range(n+1)]
for _ in xrange(n-1):
	a,b=map(int,raw_input().split())
	g[a-1]+=[(1,a-1,b-1)]
	g[b-1]+=[(1,b-1,a-1)]
z=[-1]*n
for _ in xrange(int(raw_input())):
	a,b=map(int,raw_input().split())
	g[n]+=[(b,n,a-1)]
	z[a-1]=b
a=[1e9]*n+[0]
shortestPath(g,n,a,[-1]*(n+1))
for i in xrange(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		sys.exit()
for _ in g:
	for e in _:
		if e[1]<e[2] and abs(a[e[1]]-a[e[2]])!=1:
			print('No')
			sys.exit()
print('Yes')
print("\n".join(map(str,a[:n])))

Buggy python submission (verdict: Time Limit Exceeded):
import sys
from scipy.sparse import*
g=[]
n=int(sys.stdin.readline())
for _ in xrange(n-1):
	a,b=map(int,sys.stdin.readline().split())
	g.append((a-1,b-1,1))
z=[-1]*n
for _ in xrange(int(sys.stdin.readline())):
	a,b=map(int,sys.stdin.readline().split())
	g.append((n,a-1,b))
	z[a-1]=b
a,b,c=zip(*g)
a=map(int,csgraph.dijkstra(csr_matrix((c,(a,b)),[n+1]*2),0,n))
for i in xrange(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		exit()
for e in g:
	if e[0]<e[1] and abs(a[e[0]]-a[e[1]])!=1:
		print('No')
		exit()
print('Yes')
print("\n".join(map(str,a[:n])))

Fixed submission:
#!/usr/bin/python
def shortestPath(g,s,dist,prev):
	n = len(g)-1
	Q=[]
	heapq.heappush(Q,(0,-2,s))
	while Q:
		e = heapq.heappop(Q)
		if prev[e[2]]!=-1: continue
		prev[e[2]] = e[1]
		for f in g[e[2]]:
			if dist[f[2]] > e[0] + f[0]:
				dist[f[2]] = e[0] + f[0]
				heapq.heappush(Q,(e[0]+f[0],f[1],f[2]))

import sys,heapq
#if sys.version_info[0]>=3:raw_input=input

n=int(raw_input())
g=[[] for _ in range(n+1)]
for _ in xrange(n-1):
	a,b=map(int,raw_input().split())
	g[a-1]+=[(1,a-1,b-1)]
	g[b-1]+=[(1,b-1,a-1)]
z=[-1]*n
for _ in xrange(int(raw_input())):
	a,b=map(int,raw_input().split())
	g[n]+=[(b,n,a-1)]
	z[a-1]=b
a=[1e9]*n+[0]
shortestPath(g,n,a,[-1]*(n+1))
for i in xrange(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		sys.exit()
for _ in g:
	for e in _:
		if e[1]<e[2] and abs(a[e[1]]-a[e[2]])!=1:
			print('No')
			sys.exit()
print('Yes')
print("\n".join(map(str,a[:n])))

Buggy python submission (verdict: Time Limit Exceeded):
from scipy.sparse import*
g=[]
n=int(raw_input())
for _ in xrange(n-1):
	a,b=map(int,raw_input().split())
	g.append((a-1,b-1,1))
z=[-1]*n
for _ in xrange(int(raw_input())):
	a,b=map(int,raw_input().split())
	g.append((n,a-1,b))
	z[a-1]=b
a,b,c=zip(*g)
a=map(int,csgraph.dijkstra(csr_matrix((c,(a,b)),[n+1]*2),0,n))
for i in xrange(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		exit()
for e in g:
	if e[0]<e[1] and abs(a[e[0]]-a[e[1]])!=1:
		print('No')
		exit()
print('Yes')
print("\n".join(map(str,a[:n])))

Fixed submission:
#!/usr/bin/python
def shortestPath(g,s,dist,prev):
	n = len(g)-1
	Q=[]
	heapq.heappush(Q,(0,-2,s))
	while Q:
		e = heapq.heappop(Q)
		if prev[e[2]]!=-1: continue
		prev[e[2]] = e[1]
		for f in g[e[2]]:
			if dist[f[2]] > e[0] + f[0]:
				dist[f[2]] = e[0] + f[0]
				heapq.heappush(Q,(e[0]+f[0],f[1],f[2]))

import sys,heapq
#if sys.version_info[0]>=3:raw_input=input

n=int(raw_input())
g=[[] for _ in range(n+1)]
for _ in xrange(n-1):
	a,b=map(int,raw_input().split())
	g[a-1]+=[(1,a-1,b-1)]
	g[b-1]+=[(1,b-1,a-1)]
z=[-1]*n
for _ in xrange(int(raw_input())):
	a,b=map(int,raw_input().split())
	g[n]+=[(b,n,a-1)]
	z[a-1]=b
a=[1e9]*n+[0]
shortestPath(g,n,a,[-1]*(n+1))
for i in xrange(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		sys.exit()
for _ in g:
	for e in _:
		if e[1]<e[2] and abs(a[e[1]]-a[e[2]])!=1:
			print('No')
			sys.exit()
print('Yes')
print("\n".join(map(str,a[:n])))

Buggy python submission (verdict: Time Limit Exceeded):
from scipy.sparse import*
g=[]
n=int(raw_input())
for _ in xrange(n-1):
	a,b=map(int,raw_input().split())
	g+=[(a-1,b-1,1)]
z=[-1]*n
for _ in xrange(int(raw_input())):
	a,b=map(int,raw_input().split())
	g+=[(n,a-1,b)]
	z[a-1]=b
a,b,c=zip(*g)
a=map(int,csgraph.dijkstra(csr_matrix((c,(a,b)),[n+1]*2),0,n))
for i in xrange(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		exit()
for e in g:
	if e[0]<e[1] and abs(a[e[0]]-a[e[1]])!=1:
		print('No')
		exit()
print('Yes')
print("\n".join(map(str,a[:n])))

Fixed submission:
#!/usr/bin/python
def shortestPath(g,s,dist,prev):
	n = len(g)-1
	Q=[]
	heapq.heappush(Q,(0,-2,s))
	while Q:
		e = heapq.heappop(Q)
		if prev[e[2]]!=-1: continue
		prev[e[2]] = e[1]
		for f in g[e[2]]:
			if dist[f[2]] > e[0] + f[0]:
				dist[f[2]] = e[0] + f[0]
				heapq.heappush(Q,(e[0]+f[0],f[1],f[2]))

import sys,heapq
#if sys.version_info[0]>=3:raw_input=input

n=int(raw_input())
g=[[] for _ in range(n+1)]
for _ in xrange(n-1):
	a,b=map(int,raw_input().split())
	g[a-1]+=[(1,a-1,b-1)]
	g[b-1]+=[(1,b-1,a-1)]
z=[-1]*n
for _ in xrange(int(raw_input())):
	a,b=map(int,raw_input().split())
	g[n]+=[(b,n,a-1)]
	z[a-1]=b
a=[1e9]*n+[0]
shortestPath(g,n,a,[-1]*(n+1))
for i in xrange(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		sys.exit()
for _ in g:
	for e in _:
		if e[1]<e[2] and abs(a[e[1]]-a[e[2]])!=1:
			print('No')
			sys.exit()
print('Yes')
print("\n".join(map(str,a[:n])))

Buggy python submission (verdict: Runtime Error):
from scipy.sparse import*
g=[]
n=int(raw_input())
for _ in xrange(n-1):
	a,b=map(int,raw_input().split())
	g+=[(a-1,b-1,1)]
z=[-1]*n
for _ in xrange(int(raw_input())):
	a,b=map(int,raw_input().split())
	g+=[(n,a-1,b)]
	z[a-1]=b
a,b,c=zip(*g)
a=map(int,csgraph.dijkstra(csr_matrix((c,(a,b)),[n+1]*2),0,n))
for i in xrange(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		sys.exit()
for e in g:
	if e[0]<e[1] and abs(a[e[0]]-a[e[1]])!=1:
		print('No')
		sys.exit()
print('Yes')
print("\n".join(map(str,a[:n])))

Fixed submission:
#!/usr/bin/python
def shortestPath(g,s,dist,prev):
	n = len(g)-1
	Q=[]
	heapq.heappush(Q,(0,-2,s))
	while Q:
		e = heapq.heappop(Q)
		if prev[e[2]]!=-1: continue
		prev[e[2]] = e[1]
		for f in g[e[2]]:
			if dist[f[2]] > e[0] + f[0]:
				dist[f[2]] = e[0] + f[0]
				heapq.heappush(Q,(e[0]+f[0],f[1],f[2]))

import sys,heapq
#if sys.version_info[0]>=3:raw_input=input

n=int(raw_input())
g=[[] for _ in range(n+1)]
for _ in xrange(n-1):
	a,b=map(int,raw_input().split())
	g[a-1]+=[(1,a-1,b-1)]
	g[b-1]+=[(1,b-1,a-1)]
z=[-1]*n
for _ in xrange(int(raw_input())):
	a,b=map(int,raw_input().split())
	g[n]+=[(b,n,a-1)]
	z[a-1]=b
a=[1e9]*n+[0]
shortestPath(g,n,a,[-1]*(n+1))
for i in xrange(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		sys.exit()
for _ in g:
	for e in _:
		if e[1]<e[2] and abs(a[e[1]]-a[e[2]])!=1:
			print('No')
			sys.exit()
print('Yes')
print("\n".join(map(str,a[:n])))

Buggy python submission (verdict: Runtime Error):
from heapq import*
R=range;I=lambda:map(int,input().split());n=int(input());g=[[]for _ in R(n+1)];z=[-1]*n;d=[1e9]*n+[0];q=[-1]*(n+1);r=;Q=[];heappush(Q,(0,-2,n))
for _ in R(n-1):a,b=I();a-=1;b-=1;g[a]+=[(1,a,b)];g[b]+=[(1,b,a)]
for _ in R(*I()):a,b=I();a-=1;g[n]+=[(b,n,a)];z[a]=b
while Q:
	e=heappop(Q)
	if q[e[2]]!=-1:continue
	q[e[2]]=e[1]
	for f in g[e[2]]:
		if d[f[2]]>e[0]+f[0]:d[f[2]]=e[0]+f[0];heappush(Q,(e[0]+f[0],f[1],f[2]))
for _ in g:
	if any(n!=e[1]and abs(d[e[1]]-d[e[2]])!=1 for e in _):r="No"
if any(~z[i]and z[i]!=d[i]for i in R(n)):r="No"
print(r or"Yes\n"+"\n".join(map(str,d[:n])))

Fixed submission:
#!/usr/bin/python
def shortestPath(g,s,dist,prev):
	n = len(g)-1
	Q=[]
	heapq.heappush(Q,(0,-2,s))
	while Q:
		e = heapq.heappop(Q)
		if prev[e[2]]!=-1: continue
		prev[e[2]] = e[1]
		for f in g[e[2]]:
			if dist[f[2]] > e[0] + f[0]:
				dist[f[2]] = e[0] + f[0]
				heapq.heappush(Q,(e[0]+f[0],f[1],f[2]))

import sys,heapq
#if sys.version_info[0]>=3:raw_input=input

n=int(raw_input())
g=[[] for _ in range(n+1)]
for _ in xrange(n-1):
	a,b=map(int,raw_input().split())
	g[a-1]+=[(1,a-1,b-1)]
	g[b-1]+=[(1,b-1,a-1)]
z=[-1]*n
for _ in xrange(int(raw_input())):
	a,b=map(int,raw_input().split())
	g[n]+=[(b,n,a-1)]
	z[a-1]=b
a=[1e9]*n+[0]
shortestPath(g,n,a,[-1]*(n+1))
for i in xrange(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		sys.exit()
for _ in g:
	for e in _:
		if e[1]<e[2] and abs(a[e[1]]-a[e[2]])!=1:
			print('No')
			sys.exit()
print('Yes')
print("\n".join(map(str,a[:n])))

Buggy python submission (verdict: Runtime Error):
#!/usr/bin/python
def shortestPath(g,s,dist,prev):
	n = len(g)-1
	Q=[]
	heapq.heappush(Q,(0,-2,s))
	while Q:
		e = heapq.heappop(Q)
		if prev[e[2]]!=-1: continue
		prev[e[2]] = e[1]
		for f in g[e[2]]:
			if dist[f[2]] > e[0] + f[0]:
				dist[f[2]] = e[0] + f[0]
				heapq.heappush(Q,(e[0]+f[0],f[1],f[2]))

import sys,heapq
if sys.version_info[0]>=3:raw_input=input

n=int(raw_input())
g=[[] for _ in range(n+1)]
for _ in xrange(n-1):
	a,b=map(int,raw_input().split())
	g[a-1]+=[(1,a-1,b-1)]
	g[b-1]+=[(1,b-1,a-1)]
z=[-1]*n
for _ in xrange(int(raw_input())):
	a,b=map(int,raw_input().split())
	g[n]+=[(b,n,a-1)]
	z[a-1]=b
a=[1e9]*n+[0]
shortestPath(g,n,a,[-1]*(n+1))
for i in xrange(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		sys.exit()
for _ in g:
	for e in _:
		if e[1]<e[2] and abs(a[e[1]]-a[e[2]])!=1:
			print('No')
			sys.exit()
print('Yes')
print("\n".join(map(str,a[:n])))


Fixed submission:
#!/usr/bin/python
def shortestPath(g,s,dist,prev):
	n = len(g)-1
	Q=[]
	heapq.heappush(Q,(0,-2,s))
	while Q:
		e = heapq.heappop(Q)
		if prev[e[2]]!=-1: continue
		prev[e[2]] = e[1]
		for f in g[e[2]]:
			if dist[f[2]] > e[0] + f[0]:
				dist[f[2]] = e[0] + f[0]
				heapq.heappush(Q,(e[0]+f[0],f[1],f[2]))

import sys,heapq
#if sys.version_info[0]>=3:raw_input=input

n=int(raw_input())
g=[[] for _ in range(n+1)]
for _ in xrange(n-1):
	a,b=map(int,raw_input().split())
	g[a-1]+=[(1,a-1,b-1)]
	g[b-1]+=[(1,b-1,a-1)]
z=[-1]*n
for _ in xrange(int(raw_input())):
	a,b=map(int,raw_input().split())
	g[n]+=[(b,n,a-1)]
	z[a-1]=b
a=[1e9]*n+[0]
shortestPath(g,n,a,[-1]*(n+1))
for i in xrange(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		sys.exit()
for _ in g:
	for e in _:
		if e[1]<e[2] and abs(a[e[1]]-a[e[2]])!=1:
			print('No')
			sys.exit()
print('Yes')
print("\n".join(map(str,a[:n])))

Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/python
import sys
#if sys.version_info[0]>=3:raw_input=input

from scipy.sparse import*
g=[]
n=int(raw_input())
for _ in xrange(n-1):
	a,b=map(int,raw_input().split())
	g+=[(a-1,b-1,1)]
z=[-1]*n
for _ in xrange(int(raw_input())):
	a,b=map(int,raw_input().split())
	g+=[(n,a-1,b)]
	z[a-1]=b
a,b,c=zip(*g)
a=map(int,csgraph.dijkstra(csr_matrix((c,(a,b)),[n+1]*2),0,n))
for i in xrange(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		sys.exit()
for e in g:
	if e[0]<e[1] and abs(a[e[0]]-a[e[1]])!=1:
		print('No')
		sys.exit()
print('Yes')
print("\n".join(map(str,a[:n])))

Fixed submission:
#!/usr/bin/python
def shortestPath(g,s,dist,prev):
	n = len(g)-1
	Q=[]
	heapq.heappush(Q,(0,-2,s))
	while Q:
		e = heapq.heappop(Q)
		if prev[e[2]]!=-1: continue
		prev[e[2]] = e[1]
		for f in g[e[2]]:
			if dist[f[2]] > e[0] + f[0]:
				dist[f[2]] = e[0] + f[0]
				heapq.heappush(Q,(e[0]+f[0],f[1],f[2]))

import sys,heapq
#if sys.version_info[0]>=3:raw_input=input

n=int(raw_input())
g=[[] for _ in range(n+1)]
for _ in xrange(n-1):
	a,b=map(int,raw_input().split())
	g[a-1]+=[(1,a-1,b-1)]
	g[b-1]+=[(1,b-1,a-1)]
z=[-1]*n
for _ in xrange(int(raw_input())):
	a,b=map(int,raw_input().split())
	g[n]+=[(b,n,a-1)]
	z[a-1]=b
a=[1e9]*n+[0]
shortestPath(g,n,a,[-1]*(n+1))
for i in xrange(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		sys.exit()
for _ in g:
	for e in _:
		if e[1]<e[2] and abs(a[e[1]]-a[e[2]])!=1:
			print('No')
			sys.exit()
print('Yes')
print("\n".join(map(str,a[:n])))

Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/python
import sys
#if sys.version_info[0]>=3:raw_input=input

from scipy.sparse import*
g=[]
n=int(raw_input())
for _ in xrange(n-1):
	a,b=map(int,raw_input().split())
	g+=[(a-1,b-1,1)]
	g+=[(b-1,a-1,1)]
z=[-1]*n
for _ in xrange(int(raw_input())):
	a,b=map(int,raw_input().split())
	g+=[(n,a-1,b)]
	z[a-1]=b
a,b,c=zip(*g)
a=map(int,csgraph.dijkstra(coo_matrix((c,(a,b)),[n+1]*2),1,n))
for i in xrange(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		sys.exit()
for e in g:
	if e[0]<e[1] and abs(a[e[0]]-a[e[1]])!=1:
		print('No')
		sys.exit()
print('Yes')
print("\n".join(map(str,a[:n])))

Fixed submission:
#!/usr/bin/python
def shortestPath(g,s,dist,prev):
	n = len(g)-1
	Q=[]
	heapq.heappush(Q,(0,-2,s))
	while Q:
		e = heapq.heappop(Q)
		if prev[e[2]]!=-1: continue
		prev[e[2]] = e[1]
		for f in g[e[2]]:
			if dist[f[2]] > e[0] + f[0]:
				dist[f[2]] = e[0] + f[0]
				heapq.heappush(Q,(e[0]+f[0],f[1],f[2]))

import sys,heapq
#if sys.version_info[0]>=3:raw_input=input

n=int(raw_input())
g=[[] for _ in range(n+1)]
for _ in xrange(n-1):
	a,b=map(int,raw_input().split())
	g[a-1]+=[(1,a-1,b-1)]
	g[b-1]+=[(1,b-1,a-1)]
z=[-1]*n
for _ in xrange(int(raw_input())):
	a,b=map(int,raw_input().split())
	g[n]+=[(b,n,a-1)]
	z[a-1]=b
a=[1e9]*n+[0]
shortestPath(g,n,a,[-1]*(n+1))
for i in xrange(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		sys.exit()
for _ in g:
	for e in _:
		if e[1]<e[2] and abs(a[e[1]]-a[e[2]])!=1:
			print('No')
			sys.exit()
print('Yes')
print("\n".join(map(str,a[:n])))

Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/python
import sys
#if sys.version_info[0]>=3:raw_input=input

from scipy.sparse import*
g=[]
n=int(raw_input())
for _ in xrange(n-1):
	a,b=map(int,raw_input().split())
	g+=[(a-1,b-1,1)]
	g+=[(b-1,a-1,1)]
z=[-1]*n
for _ in xrange(int(raw_input())):
	a,b=map(int,raw_input().split())
	g+=[(n,a-1,b)]
	z[a-1]=b
a,b,c=zip(*g)
a=map(int,csgraph.dijkstra(csc_matrix((c,(a,b)),[n+1]*2),1,n))
for i in xrange(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		sys.exit()
for e in g:
	if e[0]<e[1] and abs(a[e[0]]-a[e[1]])!=1:
		print('No')
		sys.exit()
print('Yes')
print("\n".join(map(str,a[:n])))

Fixed submission:
#!/usr/bin/python
def shortestPath(g,s,dist,prev):
	n = len(g)-1
	Q=[]
	heapq.heappush(Q,(0,-2,s))
	while Q:
		e = heapq.heappop(Q)
		if prev[e[2]]!=-1: continue
		prev[e[2]] = e[1]
		for f in g[e[2]]:
			if dist[f[2]] > e[0] + f[0]:
				dist[f[2]] = e[0] + f[0]
				heapq.heappush(Q,(e[0]+f[0],f[1],f[2]))

import sys,heapq
#if sys.version_info[0]>=3:raw_input=input

n=int(raw_input())
g=[[] for _ in range(n+1)]
for _ in xrange(n-1):
	a,b=map(int,raw_input().split())
	g[a-1]+=[(1,a-1,b-1)]
	g[b-1]+=[(1,b-1,a-1)]
z=[-1]*n
for _ in xrange(int(raw_input())):
	a,b=map(int,raw_input().split())
	g[n]+=[(b,n,a-1)]
	z[a-1]=b
a=[1e9]*n+[0]
shortestPath(g,n,a,[-1]*(n+1))
for i in xrange(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		sys.exit()
for _ in g:
	for e in _:
		if e[1]<e[2] and abs(a[e[1]]-a[e[2]])!=1:
			print('No')
			sys.exit()
print('Yes')
print("\n".join(map(str,a[:n])))

Buggy python submission (verdict: Time Limit Exceeded):
import sys
#if sys.version_info[0]>=3:raw_input=input

from scipy.sparse import*
g=[]
n=int(raw_input())
for _ in xrange(n-1):
	a,b=map(int,raw_input().split())
	g+=[(a-1,b-1,1)]
	g+=[(b-1,a-1,1)]
z=[-1]*n
for _ in xrange(int(raw_input())):
	a,b=map(int,raw_input().split())
	g+=[(n,a-1,b)]
	z[a-1]=b
a,b,c=zip(*g)
a=map(int,csgraph.dijkstra(csr_matrix((c,(a,b)),[n+1]*2),1,n))
for i in xrange(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		sys.exit()
for e in g:
	if e[0]<e[1] and abs(a[e[0]]-a[e[1]])!=1:
		print('No')
		sys.exit()
print('Yes')
print("\n".join(map(str,a[:n])))

Fixed submission:
#!/usr/bin/python
def shortestPath(g,s,dist,prev):
	n = len(g)-1
	Q=[]
	heapq.heappush(Q,(0,-2,s))
	while Q:
		e = heapq.heappop(Q)
		if prev[e[2]]!=-1: continue
		prev[e[2]] = e[1]
		for f in g[e[2]]:
			if dist[f[2]] > e[0] + f[0]:
				dist[f[2]] = e[0] + f[0]
				heapq.heappush(Q,(e[0]+f[0],f[1],f[2]))

import sys,heapq
#if sys.version_info[0]>=3:raw_input=input

n=int(raw_input())
g=[[] for _ in range(n+1)]
for _ in xrange(n-1):
	a,b=map(int,raw_input().split())
	g[a-1]+=[(1,a-1,b-1)]
	g[b-1]+=[(1,b-1,a-1)]
z=[-1]*n
for _ in xrange(int(raw_input())):
	a,b=map(int,raw_input().split())
	g[n]+=[(b,n,a-1)]
	z[a-1]=b
a=[1e9]*n+[0]
shortestPath(g,n,a,[-1]*(n+1))
for i in xrange(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		sys.exit()
for _ in g:
	for e in _:
		if e[1]<e[2] and abs(a[e[1]]-a[e[2]])!=1:
			print('No')
			sys.exit()
print('Yes')
print("\n".join(map(str,a[:n])))

Buggy python submission (verdict: Time Limit Exceeded):
import sys
if sys.version_info[0]>=3:raw_input=input

from scipy.sparse import*
g=[]
n=int(raw_input())
for _ in [0]*~-n:
	a,b=map(int,raw_input().split())
	g+=[[a-1,b-1,1]]
	g+=[[b-1,a-1,1]]
z=[-1]*n
for _ in [0]*int(input()):
	a,b=map(int,raw_input().split())
	g+=[[n,a-1,b]]
	z[a-1]=b
a,b,c=zip(*g)
a=map(int,csgraph.dijkstra(csr_matrix((c,(a,b)),[n+1]*2),1,n))
for i in range(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		sys.exit()
	z[i]=a[i]
for e in g:
	if e[0]!=n and abs(z[e[0]]-z[e[1]])!=1:
		print('No')
		sys.exit()
print('Yes')
print("\n".join(map(str,a[:n])))

Fixed submission:
#!/usr/bin/python
def shortestPath(g,s,dist,prev):
	n = len(g)-1
	Q=[]
	heapq.heappush(Q,(0,-2,s))
	while Q:
		e = heapq.heappop(Q)
		if prev[e[2]]!=-1: continue
		prev[e[2]] = e[1]
		for f in g[e[2]]:
			if dist[f[2]] > e[0] + f[0]:
				dist[f[2]] = e[0] + f[0]
				heapq.heappush(Q,(e[0]+f[0],f[1],f[2]))

import sys,heapq
#if sys.version_info[0]>=3:raw_input=input

n=int(raw_input())
g=[[] for _ in range(n+1)]
for _ in xrange(n-1):
	a,b=map(int,raw_input().split())
	g[a-1]+=[(1,a-1,b-1)]
	g[b-1]+=[(1,b-1,a-1)]
z=[-1]*n
for _ in xrange(int(raw_input())):
	a,b=map(int,raw_input().split())
	g[n]+=[(b,n,a-1)]
	z[a-1]=b
a=[1e9]*n+[0]
shortestPath(g,n,a,[-1]*(n+1))
for i in xrange(n):
	if z[i]>=0 and z[i]!=a[i]:
		print('No')
		sys.exit()
for _ in g:
	for e in _:
		if e[1]<e[2] and abs(a[e[1]]-a[e[2]])!=1:
			print('No')
			sys.exit()
print('Yes')
print("\n".join(map(str,a[:n])))