Given is a string S of length N.

Find the maximum length of a non-empty string that occurs twice or more in S as contiguous substrings without overlapping.

More formally, find the maximum positive integer len such that there exist integers l_1 and l_2 ( 1 \leq l_1, l_2 \leq N - len + 1 ) that satisfy the following:

* l_1 + len \leq l_2

* S[l_1+i] = S[l_2+i] (i = 0, 1, ..., len - 1)




If there is no such integer len, print 0.

Constraints

* 2 \leq N \leq 5 \times 10^3
* |S| = N
* S consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:


N
S


Output

Print the maximum length of a non-empty string that occurs twice or more in S as contiguous substrings without overlapping. If there is no such non-empty string, print 0 instead.

Examples

Input

5
ababa


Output

2


Input

2
xy


Output

0


Input

13
strangeorange


Output

5
def z_algorithm(s):
    N = len(s)
    A = [0]*N
    A[0] = N
    i,j = 1,0
    while i < N:
        while i+j < N and s[j] == s[i+j]:
            j += 1
        if j == 0:
            i += 1
            continue
        A[i] = j
        k = 1
        while i+k < N and k+A[k] < j:
            A[i+k] = A[k]
            k += 1
        i += k
        j -= k
    return A

N = int(raw_input())
S = raw_input()

ans = 0
for i in range(N):
    s = S[i:]
    lcp = z_algorithm(s)
    for j,p in enumerate(lcp):
        t = min(j, p)
        ans = max(ans, t)

print ans