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.
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.
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.
5 4
abaca
1 2
1 3
3 4
4 5
3
6 6
xzyabc
1 2
3 1
2 3
5 4
4 3
6 4
-1
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
4
1 1
f
1 1
-1
10 50
ebibwbjihv
1 10
1 2
5 4
1 8
9 7
5 6
1 8
8 7
2 6
5 4
1 9
3 2
8 3
5 6
5 9
2 4
2 7
3 9
1 2
1 7
1 10
3 7
1 8
3 10
8 6
1 7
10 6
1 6
5 8
1 5
2 10
3 9
5 8
8 3
3 7
5 2
1 10
1 4
5 3
3 2
1 2
5 8
10 4
2 10
8 2
1 9
1 8
1 2
3 4
1 8
2
13 37
dwpzcppjmhkmz
2 6
3 6
6 7
6 7
6 7
6 7
6 8
6 8
6 8
6 8
4 6
4 6
5 6
4 6
4 6
6 9
6 9
6 10
6 10
6 10
6 10
4 6
1 6
1 6
10 11
6 11
1 6
6 12
6 12
6 12
6 13
6 13
6 13
6 13
3 6
2 6
2 6
3
5 8
tetqw
2 1
4 4
5 5
5 2
4 5
1 5
1 5
1 1
-1
5 8
reeet
4 3
2 5
4 2
2 4
4 2
5 2
3 3
3 4
-1
def func1(dp,node,e,s,v):
    stack = [node]
    while stack:
        node = stack[-1]
        if node not in v:
            c= 0
            for k in e[node]:
                if k in v:
                    c+= 1
                stack.append(k)

            if c== len(e[node]):
                for k in e[node]:
                    for i in range(26):
                        dp[node][i] = max(dp[node][i],dp[k][i])

                dp[node][ord(s[node-1])-ord('a')] += 1
                v.add(node)
                stack.pop()
        else:
            stack.pop()
                    
def func2(e,node,v,r_stack):
    stack = [node]
    while stack:
        node = stack[-1]
        v.add(node)
        r_stack.add(node)
        c = 0
        for k in e[node]:
            if k not in v:
                stack.append(k)
            elif k in r_stack:
                return(True)
            else:
                c+= 1

        if c == len(e[node]):
            stack.pop()
            r_stack.remove(node)

    return False
            

def cycle(e,n):
    v = set()
    r_stack = set()
    for i in range(1,n+1):
        if i not in v:
            if func2(e,i,v,r_stack):
                return(True)

    return(False)

def beauty(n,m,s,x,y):
    e = {}
    t= set()
    for i in range(1,n+1):
        e[i] = []
    for i in range(1,n+1):
        t.add(i)
    for i in range(m):
        e[x[i]].append(y[i])
        if y[i] in t:
            t.remove(y[i])

    if cycle(e,n):
        return -1
        return

    
    visit= set()
    dp = [[0 for i in range(26)] for j in range(n+1)]
    for i in t:
        if i not in visit:
            func1(dp,i,e,s,visit)

    res= 0
    for i in t:
        res = max(res,max(dp[i]))

    return res
x=[1,1,3,4]
y=[2,3,4,5]
l=beauty(5,4,"abaca",x,y)
print(l)