题意：

在这里插入图片描述

思路：

对于第一问直接输出最长不严格下降子序列即可，第二问是Dilworth定理，变形比较多，之前也写过类似的，这里贴个证明。
在这里插入图片描述

//#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4.1,sse4.2,avx,avx2,popcnt,tune=native")
//#pragma GCC optimize(2)
#include<cstdio>
#include<iostream>
#include<string>
#include<cstring>
#include<map>
#include<cmath>
#include<cctype>
#include<vector>
#include<set>
#include<queue>
#include<algorithm>
#include<sstream>
#include<ctime>
#include<cstdlib>
#define X first
#define Y second
#define L (u<<1)
#define R (u<<1|1)
#define pb push_back
#define mk make_pair
#define Mid (tr[u].l+tr[u].r>>1)
#define Len(u) (tr[u].r-tr[u].l+1)
#define random(a,b) ((a)+rand()%((b)-(a)+1))
#define db puts("---")
using namespace std;//void rd_cre() { freopen("d://dp//data.txt","w",stdout); srand(time(NULL)); }
//void rd_ac() { freopen("d://dp//data.txt","r",stdin); freopen("d://dp//AC.txt","w",stdout); }
//void rd_wa() { freopen("d://dp//data.txt","r",stdin); freopen("d://dp//WA.txt","w",stdout); }typedef long long LL;
typedef unsigned long long ULL;
typedef pair<int,int> PII;const int N=1000010,mod=1e9+7,INF=0x3f3f3f3f;
const double eps=1e-6;int n;
int a[N],q[N];
int ans1,ans2;int main()
{
//	ios::sync_with_stdio(false);
//	cin.tie(0);while(scanf("%d",&a[++n])!=EOF);n--;int len=0;for(int i=1;i<=n;i++) {int l=0,r=len;while(l<r) {int mid=l+r+1>>1;if(q[mid]<a[i]) l=mid;else r=mid-1;}len=max(len,r+1);q[r+1]=a[i];}ans2=len;len=0; memset(q,0,sizeof(q));for(int i=n;i>=1;i--) {int l=0,r=len;while(l<r) {int mid=l+r+1>>1;if(q[mid]<a[i]) l=mid;else r=mid-1;}len=max(len,r+1);q[r+1]=a[i];}ans1=len;cout<<ans1<<endl;cout<<ans2<<endl;return 0;
}
/**/