Consider a circuit with two loops. The left loop contains a 10V battery and a 2Ω resistor. The right loop contains a 5V battery and a 1Ω resistor. The two loops share a common central branch containing a 4Ω resistor. Both batteries are oriented such that their positive terminals face the top of the circuit. Determine the magnitude and direction of the current flowing through the shared 4Ω resistor.