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 Lua (5.3.2) (judge verdict: Accepted)

local floor = math.floor
-- binary search
-- https://golang.org/src/sort/search.go?s=2246:2286#L49
local function find_min_true(n, f)
    local function loop(i, j)
        if i == j then
            return i
        end
        local h = floor((i + j) / 2)
        if f(h) then
            return loop(i, h)
        else
            return loop(h + 1, j)
        end
    end
    return loop(1, n + 1)
end


local N = io.read("*n", "*l")
local S = io.read("*l")
local sub = string.sub
local find = string.find
local function search()
    -- false if len is OK
    local function judge(len)
        for l1=1,N+1-2*len do
            local subst = sub(S, l1, l1+len-1)
            local result = find(S, subst, l1+len, true)
            --print("len", len, "l1", l1, "subst", subst, "result", result)
            if result then
                return false
            end
        end
        return true -- len is NG
    end
    return find_min_true(2500, judge)
end
local ans = search()
if ans == 0 then
    print(0)
else
    print(ans-1)
end