Jan 4 (Reuters) - The Baltic Exchange"s dry bulk sea freight index (.BADI) rose on Tuesday, crawling away from a more than eighth month low, helped by strong demand for capesize and panamax vessels. * The overall index, which factors in rates for capesize, panamax and supramax vessels, gained 68 points, or 3.1%, to 2,285, snapping a 12 session losing streak. * The capesize index (.BACI) rose 38 points, or 1.6%, to 2,350. * Average daily earnings for capesizes, which transport 150,000-tonne cargoes such as iron ore and coal, increased by $314 to $19,490. * Dalian coking coal futures rose on Tuesday to their highest level in more than two months as market participants welcomed the new year, feeling optimistic about demand prospects for the steelmaking input in top steel producer China. * The panamax index (.BPNI) added 301 points, or 11.7%, to 2,874. * Average daily earnings for panamaxes, which ferry 60,000-70,000 tonne coal or grain cargoes, rose by $2,707 to $25,865. * The supramax index (.BSIS) fell 81 points to its lowest level in more than a month at 2,209.