Six objects are placed at the vertices of a regular hexagon. The geometric center of the hexagon is at the origin with objects 1 and 4 on the x-axis(see figure). The mass of the kth object is mk​=kiM∣cosθk​∣ where i is an integer, M is a constant with dimension of mass, and θk​ is the angular position of the kth vertex measured from the positive x-axis in the counter-clockwise sense. If the net gravitational force on a body at the centroid vanishes, the value of i is?