그리디로 왜 되는지 증명을 못했다...

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

struct wood{
	int l,w;
	bool bigger(const wood &a) const
	{
		return (a.l>=l) && (a.w>=w);
	}
	bool operator<(const wood &a ) const
	{
		if(a.l==l)
			return w<a.w;
		return l<a.l;
	};
};

int main()
{
	int t;
	cin >> t;
	while(t--)
	{
		int n;
		cin >> n;
		vector<wood> a;
		a.resize(n);
		for(int i=0;i<n;i++)
			cin >> a[i].l >> a[i].w;
		sort(a.begin(), a.end());

		int cnt=0;
		while(a.size()>0)
		{
			vector<int> index;
			index.push_back(0);
			for(size_t i=1;i<a.size();i++)
				if(a[index.back()].bigger(a[i]))
					index.push_back(i);
			while(!index.empty())
			{
				a.erase(a.begin()+index.back());
				index.pop_back();				
			}
			cnt++;
		}
		cout << cnt << endl;
	}
	return 0;
}