A shipping clerk has five boxes of different but unknown weights each weighing less than $100$ kg. The clerk weighs the boxes in pairs. The weights obtained are $110, 112, 113, 114, 115, 116, 117, 118, 120$ and $121$ kg. What is the weight, in kg, of the heaviest box?
- $60$
- $62$
- $64$
- Cannot be determined