First there shouldn't be identical vertices (overlapping).

Then all paired vertices should make up either an edge (2 adjacent) or a plane (4 adjacent).

So there should be, and must be, exactly 4 vertices not paired since they are the 4 corners of the perfect rectangle.

Is this condition alone strong enough? Seems legit. Any counter testcases?

*46 / 46 test cases passed*

*Status: Accepted*

*Runtime: 139 ms*

*Beats 99.82%*

```
class Solution {
public:
bool isRectangleCover(vector<vector<int>>& rectangles) {
unordered_map<unsigned long long, uint> map;
map.reserve(rectangles.size()*4);
for (auto& rec : rectangles) {
unsigned long long xy[4];
xy[0]= (unsigned long long)rec[0] << 32 | (uint)rec[1];
xy[1]= (unsigned long long)rec[0] << 32 | (uint)rec[3];
xy[2]= (unsigned long long)rec[2] << 32 | (uint)rec[3];
xy[3]= (unsigned long long)rec[2] << 32 | (uint)rec[1];
for (uint i = 0; i < 4; i++) {
uint pos = 1 << i; //1 Left Bottom, 2 Left Top, 4 Right Top, 8 Right Bottom
uint& val = map[xy[i]];
if (val & pos) return false;
else val |= pos;
}
}
uint cnt = 0;
for (auto& p : map) {
uint pos = p.second;
if (!(pos == 1+2 || pos == 2+4 || pos == 4+8 || pos == 8+1 || pos == 1+2+4+8) && ++cnt > 4) return false;
}
return cnt == 4;
}
};
```