codeforces930C. Teodor is not a liar!上升下降子序列

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本文介绍了一种算法，用于解决一个有趣的问题：如何通过询问关于特定整数点被多少条线段覆盖的问题来判断一个人是否在关于所画线段的陈述中撒谎。该算法考虑了线段的数量和范围，通过询问最少数量的问题来确定报告者是否诚实。

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Young Teodor enjoys drawing. His favourite hobby is drawing segments with integer borders inside his huge [1;m] segment. One day Teodor noticed that picture he just drawn has one interesting feature: there doesn't exist an integer point, that belongs each of segments in the picture. Having discovered this fact, Teodor decided to share it with Sasha.

Sasha knows that Teodor likes to show off so he never trusts him. Teodor wants to prove that he can be trusted sometimes, so he decided to convince Sasha that there is no such integer point in his picture, which belongs to each segment. However Teodor is lazy person and neither wills to tell Sasha all coordinates of segments' ends nor wills to tell him their amount, so he suggested Sasha to ask him series of questions 'Given the integer point x_i, how many segments in Fedya's picture contain that point?', promising to tell correct answers for this questions.

Both boys are very busy studying and don't have much time, so they ask you to find out how many questions can Sasha ask Teodor, that having only answers on his questions, Sasha can't be sure that Teodor isn't lying to him. Note that Sasha doesn't know amount of segments in Teodor's picture. Sure, Sasha is smart person and never asks about same point twice.

Input

First line of input contains two integer numbers: n and m (1 ≤ n, m ≤ 100 000) — amount of segments of Teodor's picture and maximal coordinate of point that Sasha can ask about.

ith of next n lines contains two integer numbers l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — left and right ends of ith segment in the picture. Note that that left and right ends of segment can be the same point.

It is guaranteed that there is no integer point, that belongs to all segments.

Output

Single line of output should contain one integer number k – size of largest set (x_i, cnt(x_i)) where all x_i are different, 1 ≤ x_i ≤ m, and cnt(x_i) is amount of segments, containing point with coordinate x_i, such that one can't be sure that there doesn't exist point, belonging to all of segments in initial picture, if he knows only this set(and doesn't know n).

Examples

Input

Copy

2 4
1 2
3 4

Output

Copy

Input

Copy

Output

Copy

Note

First example shows situation where Sasha can never be sure that Teodor isn't lying to him, because even if one knows cnt(x_i) for each point in segment [1;4], he can't distinguish this case from situation Teodor has drawn whole [1;4] segment.

In second example Sasha can ask about 5 points e.g. 1, 2, 3, 5, 6, still not being sure if Teodor haven't lied to him. But once he knows information about all points in [1;6] segment, Sasha can be sure that Teodor haven't lied to him.

#include<bits/stdc++.h>
using namespace std;

#define ll long long
#define rep(i,a,n) for(int i=a;i<n;i++)

ll rd(){
    ll x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}

const int inf=0x3f3f3f3f;
const int N=1e5+10;
int l2l[N];

void solve(int val[],int dp[],int m){
    rep(i,1,m+1)
        l2l[i]=inf;
    rep(i,0,m){
        int x=val[i];
        int pos=upper_bound(l2l,l2l+m,x)-l2l;
        l2l[pos]=min(l2l[pos],x);
        dp[i]=pos;
    }
}

int val[N];
int dp[N],dpr[N];

int main(){
    freopen("in.txt","r",stdin);
    int n=rd(),m=rd();
    rep(i,0,n){
        int l=rd(),r=rd();
        val[l-1]++;
        val[r]--;
    }
    rep(i,0,m)
    val[i+1]+=val[i];
    solve(val,dp,m);
    reverse(val,val+m);
    solve(val,dpr,m);
    reverse(dpr,dpr+m);
    int ans=0;
    rep(i,0,m)
    ans=max(ans,dp[i]+dpr[i]-1);
    cout<<ans<<endl;

}