Dilworth theorem

The number of a chain in a sequence = The length of the longest anti chain in this sequence

The number of longest non ascending subsequences = The length of the longest ascending subsequence

Number of longest ascending subsequences = The longest Non rising subsequence length

The length can be found

The longest Non rising subsequence length

 g[++ans]=w[1];
    for(int i=2;i<=n;i++)
    {
        if(w[i]<=g[ans])g[++ans]=w[i];
        else
        {
            int x=upper_bound(g+1,g+ans+1,w[i],greater<int>())-g;
            g[x]=w[i];
        }
    }

The length of the longest ascending subsequence

f[++cnt] = w[1];
    for (int i = 2; i <=n; i++)
    {
        if (w[i] > f[cnt]) f[++cnt] = w[i];
        else
        {
            int x=lower_bound(f+1,f+cnt+1,w[i])-f;
            f[x]=w[i];
        }

    }