OPM 2014 Problem 1

The ship Meridiano do Bacalhau does its fishing business during $64$ days. Each day the capitain chooses a direction which may be either north or south and the ship sails that direction in that day. On the first day of business the ship sails $1$ mile, on the second day sails $2$ miles; generally, on the $n$ -th day it sails $n$ miles. After of the $64$ -th day, the ship was $2014$ miles north from its initial position. What is the greatest number of days that the ship could have sailed south?