You are given a graph with $n$ nodes and $m$ directed edges. One lowercase letter is assigned to each node. We define a path's value as the number of the most frequently occurring letter. For example, if letters on a path are "abaca", then the value of that path is $3$. Your task is find a path whose value is the largest.


-----Input-----

The first line contains two positive integers $n, m$ ($1 \leq n, m \leq 300\,000$), denoting that the graph has $n$ nodes and $m$ directed edges.

The second line contains a string $s$ with only lowercase English letters. The $i$-th character is the letter assigned to the $i$-th node.

Then $m$ lines follow. Each line contains two integers $x, y$ ($1 \leq x, y \leq n$), describing a directed edge from $x$ to $y$. Note that $x$ can be equal to $y$ and there can be multiple edges between $x$ and $y$. Also the graph can be not connected.


-----Output-----

Output a single line with a single integer denoting the largest value. If the value can be arbitrarily large, output -1 instead.


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

Output
3

Input
6 6
xzyabc
1 2
3 1
2 3
5 4
4 3
6 4

Output
-1

Input
10 14
xzyzyzyzqx
1 2
2 4
3 5
4 5
2 6
6 8
6 5
2 10
3 9
10 9
4 6
1 10
2 8
3 7

Output
4



-----Note-----

In the first sample, the path with largest value is $1 \to 3 \to 4 \to 5$. The value is $3$ because the letter 'a' appears $3$ times.

Difficulty: interview

Starter code:

Solutions:
# NOT MY CODE
# https://codeforces.com/contest/919/submission/80857731
 
from types import GeneratorType
 
def bootstrap(f, stack=[]):
    def wrappedfunc(*args, **kwargs):
        to = f(*args, **kwargs)
        if stack:
            return to
        else:
            while True:
                if type(to) is GeneratorType:
                    stack.append(to)
                    to = next(to)
                else:
                    stack.pop()
                    if not stack:
                        return to
                    to = stack[-1].send(to)
    return wrappedfunc
 
import sys
input=sys.stdin.readline
from collections import defaultdict as dd
'''
def iscyclic(g):
    for i in range(1,n+1):
        if(
'''
n,m=list(map(int,input().split()))
s=input()
d=dd(list)
lol=0
for i in range(m):
    u,v=list(map(int,input().split()))
    if(u==v):
        lol=1
        print(-1)
        return
    d[u].append(v)
'''
if(iscyclic(d)):
    lol=1
    print(-1)
    return
'''
vis=[0]*(n+1)
rvis=[0]*(n+1)
cou=[0]
dp=[dd(int) for i in range(n+1)]
mx=[0]
h=[0]
#print(d)
@bootstrap
def dfs(u):
    if(h[0]==1):
        yield
    vis[u]=1
    rvis[u]=1
    for i in d[u]:
        if(h[0]==1):
            yield
        if(vis[i]==0):
            yield dfs(i)
            if(h[0]==1):
                yield            
        elif(rvis[i]==True):
            h[0]=1
            yield
    rvis[u]=0
    if(h[0]==1):
        yield
    for i in d[u]:
        for j in dp[i]:
            dp[u][j]=max(dp[u][j],dp[i][j])
            mx[0]=max(mx[0],dp[u][j])
    dp[u][s[u-1]]+=1
    #print(u,dp[u])
    mx[0]=max(mx[0],dp[u][s[u-1]])
    yield
#print(dp)
for i in range(1,n+1):
    if(vis[i]==0):
        cou=[0]
        dfs(i)
if(h[0]):
    print(-1)
else:
    print(mx[0])


from types import GeneratorType
 
def bootstrap(f, stack=[]):
    def wrappedfunc(*args, **kwargs):
        to = f(*args, **kwargs)
        if stack:
            return to
        else:
            while True:
                if type(to) is GeneratorType:
                    stack.append(to)
                    to = next(to)
                else:
                    stack.pop()
                    if not stack:
                        return to
                    to = stack[-1].send(to)
    return wrappedfunc
 
import sys
input=sys.stdin.readline
from collections import defaultdict as dd
'''
def iscyclic(g):
    for i in range(1,n+1):
        if(
'''
n,m=map(int,input().split())
s=input()
d=dd(list)
lol=0
for i in range(m):
    u,v=map(int,input().split())
    if(u==v):
        lol=1
        print(-1)
        return
    d[u].append(v)
'''
if(iscyclic(d)):
    lol=1
    print(-1)
    return
'''
vis=[0]*(n+1)
rvis=[0]*(n+1)
cou=[0]
dp=[dd(int) for i in range(n+1)]
mx=[0]
h=[0]
#print(d)
@bootstrap
def dfs(u):
    if(h[0]==1):
        yield
    vis[u]=1
    rvis[u]=1
    for i in d[u]:
        if(h[0]==1):
            yield
        if(vis[i]==0):
            yield dfs(i)
            if(h[0]==1):
                yield            
        elif(rvis[i]==True):
            h[0]=1
            yield
    rvis[u]=0
    if(h[0]==1):
        yield
    for i in d[u]:
        for j in dp[i]:
            dp[u][j]=max(dp[u][j],dp[i][j])
            mx[0]=max(mx[0],dp[u][j])
    dp[u][s[u-1]]+=1
    #print(u,dp[u])
    mx[0]=max(mx[0],dp[u][s[u-1]])
    yield
#print(dp)
for i in range(1,n+1):
    if(vis[i]==0):
        cou=[0]
        dfs(i)
if(h[0]):
    print(-1)
else:
    print(mx[0])

from sys import stdin
input=lambda : stdin.readline().strip()
from math import ceil,sqrt,factorial,gcd
from collections import deque
from bisect import bisect_left
n,m=map(int,input().split())
l=list(input())
degree=[0 for i in range(n)]
graph={i:[] for i in range(n)}
for i in range(m):
	a,b=map(int,input().split())
	a-=1
	b-=1
	graph[a].append(b)
	degree[b]+=1
q=deque()
for i in range(n):
	if degree[i]==0:
		q.append(i)
count=0
ans=0
# print(degree)
dp=[[0 for i in range(26)] for i in range(n)]
while count<n and q:
	x=q.popleft()
	count+=1
	# print(ord(l[x])-97)
	dp[x][ord(l[x])-97]+=1
	for i in graph[x]:
		for j in range(26):
			dp[i][j]=max(dp[i][j],dp[x][j])
		degree[i]-=1
		if degree[i]==0:
			q.append(i)
# print(degree)
if count!=n:
	print(-1)
else:
	ans=0
	for i in range(n):
		ans=max(ans,max(dp[i]))
	print(ans)

from sys import stdin
input=lambda : stdin.readline().strip()
from math import ceil,sqrt,factorial,gcd
from collections import deque
from bisect import bisect_left
n,m=list(map(int,input().split()))
l=list(input())
degree=[0 for i in range(n)]
graph={i:[] for i in range(n)}
for i in range(m):
	a,b=list(map(int,input().split()))
	a-=1
	b-=1
	graph[a].append(b)
	degree[b]+=1
q=deque()
for i in range(n):
	if degree[i]==0:
		q.append(i)
count=0
ans=0
# print(degree)
dp=[[0 for i in range(26)] for i in range(n)]
while count<n and q:
	x=q.popleft()
	count+=1
	# print(ord(l[x])-97)
	dp[x][ord(l[x])-97]+=1
	for i in graph[x]:
		for j in range(26):
			dp[i][j]=max(dp[i][j],dp[x][j])
		degree[i]-=1
		if degree[i]==0:
			q.append(i)
# print(degree)
if count!=n:
	print(-1)
else:
	ans=0
	for i in range(n):
		ans=max(ans,max(dp[i]))
	print(ans)


from sys import stdin
input=lambda : stdin.readline().strip()
from math import ceil,sqrt,factorial,gcd
from collections import deque
from bisect import bisect_left
n,m=list(map(int,input().split()))
s=input()
x=[]
y=[]
for i in range(m):
    a,b=list(map(int,input().split()))
    x.append(a)
    y.append(b)

def beauty(n,m,s,x,y):
    l=list(s)
    degree=[0 for i in range(n)]
    graph={i:[] for i in range(n)}
    for i in range(m):
        a,b=x[i],y[i]
        a-=1
        b-=1
        graph[a].append(b)
        degree[b]+=1
    q=deque()
    for i in range(n):
        if degree[i]==0:
            q.append(i)
    
    count=0
    ans=0
    # print(degree)
    dp=[[0 for i in range(26)] for i in range(n)]
    while count<n and q:
            x=q.popleft()
            count+=1
            # print(ord(l[x])-97)
            dp[x][ord(l[x])-97]+=1
            for i in graph[x]:
                    for j in range(26):
                            dp[i][j]=max(dp[i][j],dp[x][j])
                    degree[i]-=1
                    if degree[i]==0:
                            q.append(i)
    # print(degree)
    if count!=n:
            print(-1)
    else:
            ans=0
            for i in range(n):
                    ans=max(ans,max(dp[i]))
            print(ans)

beauty(n,m,s,x,y)


from sys import stdin
input=lambda : stdin.readline().strip()
from math import ceil,sqrt,factorial,gcd
from collections import deque
from bisect import bisect_left
n,m=list(map(int,input().split()))
s=input()
x=[]
y=[]
for i in range(m):
    a,b=list(map(int,input().split()))
    x.append(a)
    y.append(b)

def beauty(n,m,s,x,y):
    l=list(s)
    degree=[0 for i in range(n)]
    graph={i:[] for i in range(n)}
    for i in range(m):
        a,b=x[i],y[i]
        a-=1
        b-=1
        graph[a].append(b)
        degree[b]+=1
    q=deque()
    for i in range(n):
        if degree[i]==0:
            q.append(i)
    
    count=0
    ans=0
    # print(degree)
    dp=[[0 for i in range(26)] for i in range(n)]
    while count<n and q:
            x=q.popleft()
            count+=1
            # print(ord(l[x])-97)
            dp[x][ord(l[x])-97]+=1
            for i in graph[x]:
                    for j in range(26):
                            dp[i][j]=max(dp[i][j],dp[x][j])
                    degree[i]-=1
                    if degree[i]==0:
                            q.append(i)
    # print(degree)
    if count!=n:
            print(-1)
    else:
            ans=0
            for i in range(n):
                    ans=max(ans,max(dp[i]))
            print(ans)

beauty(n,m,s,x,y)