You are given an undirected tree of $n$ vertices. 

Some vertices are colored blue, some are colored red and some are uncolored. It is guaranteed that the tree contains at least one red vertex and at least one blue vertex.

You choose an edge and remove it from the tree. Tree falls apart into two connected components. Let's call an edge nice if neither of the resulting components contain vertices of both red and blue colors.

How many nice edges are there in the given tree?


-----Input-----

The first line contains a single integer $n$ ($2 \le n \le 3 \cdot 10^5$) — the number of vertices in the tree.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 2$) — the colors of the vertices. $a_i = 1$ means that vertex $i$ is colored red, $a_i = 2$ means that vertex $i$ is colored blue and $a_i = 0$ means that vertex $i$ is uncolored.

The $i$-th of the next $n - 1$ lines contains two integers $v_i$ and $u_i$ ($1 \le v_i, u_i \le n$, $v_i \ne u_i$) — the edges of the tree. It is guaranteed that the given edges form a tree. It is guaranteed that the tree contains at least one red vertex and at least one blue vertex.


-----Output-----

Print a single integer — the number of nice edges in the given tree.


-----Examples-----
Input
5
2 0 0 1 2
1 2
2 3
2 4
2 5

Output
1

Input
5
1 0 0 0 2
1 2
2 3
3 4
4 5

Output
4

Input
3
1 1 2
2 3
1 3

Output
0



-----Note-----

Here is the tree from the first example: [Image] 

The only nice edge is edge $(2, 4)$. Removing it makes the tree fall apart into components $\{4\}$ and $\{1, 2, 3, 5\}$. The first component only includes a red vertex and the second component includes blue vertices and uncolored vertices.

Here is the tree from the second example: [Image] 

Every edge is nice in it.

Here is the tree from the third example: [Image] 

Edge $(1, 3)$ splits the into components $\{1\}$ and $\{3, 2\}$, the latter one includes both red and blue vertex, thus the edge isn't nice. Edge $(2, 3)$ splits the into components $\{1, 3\}$ and $\{2\}$, the former one includes both red and blue vertex, thus the edge also isn't nice. So the answer is 0.

Difficulty: introductory

Starter code:

Solutions:
import sys


n = int(input())
a = [int(t) for t in input().split(' ')]
mx = [[] for _ in range(n)]

lines = sys.stdin.readlines()
for i in range(n-1):
    v1, v2 = (int(t) - 1 for t in lines[i].split(' '))
    mx[v1].append(v2)
    mx[v2].append(v1)

count = [[0, 0] for _ in range(n)]

total = [a.count(1), a.count(2)]
answer = 0

OBSERVE = 0
CHECK = 1

stack = [(OBSERVE, 0, -1)]
while len(stack):
    state, v, from_ = stack.pop()
    if state == OBSERVE:
        stack.append((CHECK, v, from_))
        for nv in mx[v]:
            if nv != from_:
                stack.append((OBSERVE, nv, v))
    else:
        for nv in mx[v]:
            if nv != from_:
                if count[nv][0] == total[0] and count[nv][1] == 0 or count[nv][1] == total[1] and count[nv][0] == 0:
                    answer += 1
                count[v][0] += count[nv][0]
                count[v][1] += count[nv][1]

        if a[v] != 0:
            count[v][a[v]-1] += 1

print(answer)


import sys
from collections import defaultdict
n = int(input())
#n,k = [int(__) for __ in raw_input().split()]
arr = [int(__) for __ in input().split()]
sactive = set()
sactive.add(0)
nums = [0] * n
d1 = defaultdict(set)
d2 = defaultdict(set)
d = defaultdict(set)
lines = sys.stdin.readlines()
for i in range(n-1):
    sactive.add(i+1)
    s,f = [int(__) for __ in lines[i].strip().split()]
    s -= 1
    f -= 1
    d[s].add(f)
    d[f].add(s)
    nums[f] += 1
    nums[s] += 1

leaves = set()



for i in range(n):
    if nums[i] == 1:
        leaves.add(i)
while len(leaves):
    x = leaves.pop()
    if arr[x] == 0:
        sactive.remove(x)
        nums[x] -= 1
        targ = d[x].pop()
        nums[targ] -= 1
        d[targ].remove(x)
        if nums[targ] == 1:
            leaves.add(targ)

sactive1 = sactive.copy()
for targ in d:
    d1[targ] = d[targ].copy()
nums1 = nums[:]
nums2 = nums[:]

for i in range(n):
    if nums1[i] == 1:
        leaves.add(i)
while len(leaves):
    x = leaves.pop()
    if arr[x] != 1:
        sactive1.remove(x)
        nums1[x] -= 1
        targ = d1[x].pop()
        nums1[targ] -= 1
        d1[targ].remove(x)
        if nums1[targ] == 1:
            leaves.add(targ)
            
sactive2 = sactive.copy()
for targ in d:
    d2[targ] = d[targ].copy()

for i in range(n):
    if nums2[i] == 1:
        leaves.add(i)
while len(leaves):
    x = leaves.pop()
    if arr[x] != 2:
        sactive2.remove(x)
        nums2[x] -= 1
        targ = d2[x].pop()
        nums2[targ] -= 1
        d2[targ].remove(x)
        if nums2[targ] == 1:
            leaves.add(targ)

           
if len(sactive1 & sactive2) > 0:
    print(0)
else:
    print(len(sactive) - len(sactive1) - len(sactive2) + 1)
#print(nums)
#print('both',sactive)
#print('1',sactive1)
#print('2',sactive2)
#print(d)


import sys
input=sys.stdin.readline
n = int(input())
a = [int(t) for t in input().split(' ')]
mx = [[] for _ in range(n)]
for i in range(n-1):
    v1, v2 = list(map(int,input().split()))
    mx[v1-1].append(v2-1)
    mx[v2-1].append(v1-1)
count = [[0, 0] for _ in range(n)]
total = [a.count(1), a.count(2)]
answer = 0
OBSERVE = 0
CHECK = 1
stack = [(OBSERVE, 0, -1)]
while len(stack):
    #print(stack,count)
    state, vertex, parent = stack.pop()
    if state == OBSERVE:
        stack.append((CHECK, vertex, parent))
        for child in mx[vertex]:
            #print(nv,v,from_)
            if child != parent:
                stack.append((OBSERVE, child, vertex))
    else:
        for child in mx[vertex]:
            if child != parent:
                #print(child,parent,count)
                if count[child][0] == total[0] and count[child][1] == 0 or count[child][1] == total[1] and count[child][0] == 0:
                    answer += 1
                count[vertex][0] += count[child][0]
                count[vertex][1] += count[child][1]
 
        if a[vertex] != 0:
            #print(count)
            count[vertex][a[vertex]-1] += 1
            #print(count)
 
print(answer)


from collections import deque
import sys
input = sys.stdin.readline

class Graph(object):
	"""docstring for Graph"""
	def __init__(self,n,d): # Number of nodes and d is True if directed
		self.n = n
		self.graph = [[] for i in range(n)]
		self.parent = [-1 for i in range(n)]
		self.directed = d
		
	def addEdge(self,x,y):
		self.graph[x].append(y)
		if not self.directed:
			self.graph[y].append(x)

	def bfs(self, root): # NORMAL BFS
		self.parent = [-1 for i in range(self.n)]
		queue = [root]
		queue = deque(queue)
		vis = [0]*self.n
		while len(queue)!=0:
			element = queue.popleft()
			vis[element] = 1
			for i in self.graph[element]:
				if vis[i]==0:
					queue.append(i)
					self.parent[i] = element

	def dfs(self, root, ans): # Iterative DFS
		stack=[root]
		vis=[0]*self.n
		stack2=[]
		while len(stack)!=0: # INITIAL TRAVERSAL
			element = stack.pop()
			if vis[element]:
				continue
			vis[element] = 1
			stack2.append(element)
			for i in self.graph[element]:
				if vis[i]==0:
					self.parent[i] = element
					stack.append(i)

		while len(stack2)!=0: # BACKTRACING. Modify the loop according to the question
			element = stack2.pop()
			m = [0,0]
			for i in self.graph[element]:
				if i!=self.parent[element]:
					m[0] += ans[i][0]
					m[1] += ans[i][1]
			if arr[element] == 1:
				m[0] += 1
			elif arr[element] == 2:
				m[1] += 1
			ans[element] = m
		return ans

	def shortestpath(self, source, dest): # Calculate Shortest Path between two nodes
		self.bfs(source)
		path = [dest]
		while self.parent[path[-1]]!=-1:
			path.append(parent[path[-1]])
		return path[::-1]

	def ifcycle(self):
		self.bfs(0)
		queue = [0]
		vis = [0]*n
		queue = deque(queue)
		while len(queue)!=0:
			element = queue.popleft()
			vis[element] = 1
			for i in graph[element]:
				if vis[i]==1 and i!=parent[element]:
					return True
				if vis[i]==0:
					queue.append(i)
					vis[i] = 1
		return False

	def reroot(self, root, ans):
		stack = [root]
		count = 0
		vis = [0]*self.n
		while len(stack)!=0:
			e = stack[-1]
			# print (e,ans)
			if vis[e]:
				stack.pop()
				if self.parent[e]!=-1:
					ans[self.parent[e]][0] += ans[e][0]
					ans[self.parent[e]][1] += ans[e][1]
					if self.parent[self.parent[e]]!=-1:
						ans[self.parent[e]][0] -= ans[self.parent[self.parent[e]]][0]
						ans[self.parent[e]][1] -= ans[self.parent[self.parent[e]]][1]
				continue
			vis[e]=1
			for i in self.graph[e]:
				if not vis[i]:
					stack.append(i)
			if self.parent[e]==-1:
				continue
			ans[self.parent[e]][0] -= ans[e][0]
			ans[self.parent[e]][1] -= ans[e][1]
			if self.parent[self.parent[e]]!=-1:
				ans[self.parent[e]][0] += ans[self.parent[self.parent[e]]][0]
				ans[self.parent[e]][1] += ans[self.parent[self.parent[e]]][1]
			if 0 in ans[e] and 0 in ans[self.parent[e]]:
				count+=1
		return count


n = int(input())
g = Graph(n,False)
arr = list(map(int,input().split()))
for i in range(n-1):
	x,y = list(map(int,input().split()))
	g.addEdge(x-1,y-1)
ans = [[0,0] for i in range(n)]
a = g.dfs(0,ans)
print(g.reroot(0,a))