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 dffs(t,node,edg,s,visit):
    st = [node]
    while st:
        node = st[-1]
        if node not in visit:
            count = 0
            for k in edg[node]:
                if k in visit:
                    count+=1
                st.append(k)
            if count == len(edg[node]):
                for k in edg[node]:
                    for i in range(26):
                        t[node][i] = max(t[node][i],t[k][i])
                    t[node][ord(s[node -1]) - ord('a')+=1
                    visit.add(node)
                    st.pop()
            else:
                st.pop()
def dffs2(edges,node,visit,st_re):
    stack = [node]
    while stack:
        node = stack[-1]
        visit.add(node)
        st_re.add(node)
        count = 0
        for k in edges[node]:
            if k not in visit:
                stack.append(k)
            elif k in st_re:
                return True
            else:
                count+=1
            if count ==len(edges[node]):
                stack.pop()
                st_re.remove(node)
        return False
def cycle(edg,n):
    visit = set()
    st_rec = set()
    for i in range(1,n+1):
        if i not in visit:
            if dffs2(edg,i,visit,st_rec):
                return True
    return False
def beauty(n,m,s,x,y):
    edg = {}
    for i in range(1,n+1):
        edg[i] = []
    p = set()
    for i in range(1,n+1):
        p.add(i)
    for i in range(m):
        edg[x[i]].append(y[i])
        if y[i] in p:
            p.remove(y[i])
        if cycle(edg,n):
            return(-1)
            return
        t = [[0 for i in range(26)] for j in range(n+1)]
        visit = set()
        for i in p:
            if i not in visit:
                dffs(t,i,edg,s,visit)
        result = 0
        for i in p:
            result = max(result,max(t[i]))
        return result