Problem:
Score : 500 points

Problem Statement

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.

Sample Input 1

5
ababa

Sample Output 1

2

The strings satisfying the conditions are: a, b, ab, and ba. The maximum length among them is 2, which is the answer.
Note that aba occurs twice in S as contiguous substrings, but there is no pair of integers l_1 and l_2 mentioned in the statement such that l_1 + len \leq l_2.

Sample Input 2

2
xy

Sample Output 2

0

No non-empty string satisfies the conditions.

Sample Input 3

13
strangeorange

Sample Output 3

5

Solution in Python (3.4.3) (judge verdict: Time Limit Exceeded)

import sys,collections as cl,bisect as bs,heapq as hq
sys.setrecursionlimit(100000)
def l(): #intのlist
    return list(map(int,input().split()))
def m(): #複数文字
    return map(int,input().split())
def onem(): #Nとかの取得
    return int(input())
def jo(x): #listをスペースごとに分ける
    return " ".join(map(str,x))
def In(x,a): #aがリスト(sorted)
    k = bs.bisect_left(a,x)
    if k != len(a) and a[k] ==  x:
        return True
    else:
        return False

def search(a,n):
    se = dict()
    data = []
    for i in range(0,len(a)-n+1):
        kkk = a[i:i+n]
        kkk = "".join(kkk)
        if In(kkk,data):
            for j in range(len(se[kkk])):
                if se[kkk][j] <= i-n:
                    return True
            else:
                se[kkk].append(i)
        else:
            bs.insort(data,kkk)
            se[kkk] = [i]
    return False
def solver():
    n = onem()

    s = list(input())
    l = 0
    r = n//2
    for i in range(n):
        mid = -(-(l+r)//2)
        ans = search(s,mid)
        if l == mid:
            break
        if ans:
            l = mid
        else:
            r = mid-1
    print(l)




solver()