Recover a shared secret

Cryptographic protocols, Autumn 2009, 5th home exercise

A dealer used Shamir's secret sharing scheme to share a secret v among ten parties, such that any four of them could recover it. The secret value, as well as the shares of parties belong to the field Z13. At the recovery time, the parties reported the following shares:
P1 12
P2 8
P3 2
P4 11
P5 0
P6 7
P7 9
P8 4
P9 5
P10 10
(the value reported by Pi is the value of the sharing polynomial at the point i).

It is known that up to three parties may have lied when reporting the value of their share. Find v.