Suppose there are 160 pigeons and n holes. The 1st pigeon flies to the 1st hole, the 2nd pigeon flies to the 4th hole, and so on, such that the ith pigeon flies to the \left(i^{2} \bmod n\right) th hole, where k \bmod n is the remainder when k is divided by n. What is minimum n such that there is at most one pigeon per hole?