I Promised to Fight for the Living

**Jaime Lannister** has abandoned his sister and lover **Cersei**, and now has come to Winterfell to fight against **the army of the dead**. He along with others has to study the weaknesses of White Waker Army. This can be done by monitoring $N$ strings. The $N$ strings are $A_1, A_2, \ldots, A_N$. $A_i$ is said to be the string with index $i$. He with Bronn has to make a **set S compri