CF-Approximating a Constant Range

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Description

When Xellos was doing a practice course in university, he once had to measure the intensity of an effect that slowly approached equilibrium. A good way to determine the equilibrium intensity would be choosing a sufficiently large number of consecutive data points that seems as constant as possible and taking their average. Of course, with the usual sizes of data, it‘s nothing challenging — but why not make a similar programming contest problem while we‘re at it?

You‘re given a sequence of n data points a_{1, ..., an. There aren‘t any big jumps between consecutive data points — for each 1 ≤ i < n, it‘s guaranteed that |ai + 1 - ai| ≤ 1.}

A range [l, r] of data points is said to be almost constant if the difference between the largest and the smallest value in that range is at most 1. Formally, let M be the maximum and m the minimum value of a_{i for l ≤ i ≤ r; the range [l, r] is almost constant if M - m ≤ 1.}

Find the length of the longest almost constant range.

Input

The first line of the input contains a single integer n (2 ≤ n ≤ 100 000) — the number of data points.

The second line contains n integers a_{1, a2, ..., an (1 ≤ ai ≤ 100 000).}

Output

Print a single number — the maximum length of an almost constant range of the given sequence.

Sample Input

Input

5
1 2 3 3 2

Output

4

Input

11
5 4 5 5 6 7 8 8 8 7 6

Output

5

Hint

In the first sample, the longest almost constant range is [2, 5]; its length (the number of data points in it) is 4.

In the second sample, there are three almost constant ranges of length 4: [1, 4], [6, 9] and [7, 10]; the only almost constant range of the maximum length 5 is [6, 10].

思路：

一開始各種想LIS，但是CF再次證明了前兩道題目全是想法題（雖然想法並不比演算法簡單= =~）

首先是要在一整個數段中找到其中的一個子數段，在它的M-m<=1的情況下使其len最大

那麼這裡就涉及到兩個思維的關鍵點：

（1）不同狀態之間的轉換：為每個狀態設定一個M和m，對於每一個後進入的點判斷是否可以繼續維持前一狀態，如果可以就count++

（2）要意識到新狀態的開始點並不一定是舊狀態的結束點：可能有一點使得原來的狀態不能夠持續下去而結束了，但是並不意味著這一點就是新狀態的開始點，在維持舊狀態的過程中可能就出現了新狀態的開始點，這點主要到了以後只要根據不同的情況去找那個開始點就OK了

 

#include <iostream>using namespace std;int m,M,n;int num[100007];bool ok(int t){    if(m==M) {        if(t==m)            return true;        else if(t == m-1||t == m+1)            return true;        else             return false;    }    else {        if(t==M||t==m)            return true;        else             return false;    }}int main(){    while(cin>>n)    {        cin>>num[1];        m = num[1];        M = num[1];        int count = 1;        int ans = 0;        for(int i = 2;i <= n;i++)        {            cin>>num[i];            if(ok(num[i]))            {                if(m==M && num[i] == m-1)                     m = num[i];                else if(m==M && num[i] == m+1)                    M = num[i];                count++;            }            else {                if(m == M) {                    M = m = num[i];                    count = 1;                }                else {                    int pos;                    if(num[i] == num[i-1]+1) {                        M = num[i];                        m = num[i-1];                        for(int j = i-1;j >= 1;j--)                        {                            if(num[j] != num[i-1])                                break;                            pos = j;                        }                        count = i-pos+1;//此時的count應該=當前的座標-s段開始的座標                     }                    else if(num[i] == num[i-1]-1) {                        M = num[i-1];                        m = num[i];                        for(int j = i-1;j >= 1;j--)                        {                            if(num[j] != num[i-1])                                break;                            pos = j;                        }                        count = i-pos+1;//同上                     }                    else {                        M = m = num[i];                        count = 1;                    }                }            }            ans = max(ans,count);        }            cout<<ans<<endl;    }    return 0;}

CF-Approximating a Constant Range