When Mrs. Bethany Kieron died, the net worth of all her belongings amounted to six million dollars. In her will, she instructed that it be divided equally among her seven children. Some of the children took their portion in cash. Others preferred to inherit their mother's possessions, whose worth had been appraised by her attorneys. Her son William wanted his portion of the inheritance to come from his mother's extensive collection of contemporary impressionist paintings, each of which is valued at a quarter of a million dollars. How many of the paintings could he inherit without exceeding his fair share?