SAN JOSE MINE, Chile— A new video of 33 men trapped in a mine under Chile's Atacama Desert shows them sending greetings to their families, talking about how they are doing better since receiving food and breaking into tears as they talk about loved ones.In the video released Sunday, the men are shirtless because of the heat in the mine and wearing what look like white surgical pants, special clothing sent down to help keep them dry.Most are upbeat, expressing gratitude to their families and the rescuers for the support they are receiving via handwritten notes sent to them through three small bore holes. Authorities also send food, water, medicine and other goods to them through the three holes.But when it comes time to speak about their wives and children, many of the men break down.Araya and 32 fellow miners were trapped by the Aug. 5 collapse of the main shaft of the San Jose gold and silver mine in northern Chile. They only gained contact with the outside after 17 days — during which they rationed 48-hours' worth of food and dug for water in the ground. On Monday, the men will equal a mark set by three miners who survived 25 days trapped in a flooded mine in southern China last year. Few other rescues have taken more than two weeks.The miners will have to aid in their own escape by clearing thousands of tons of rock that will fall as a rescue hole is drilled toward them."The miners are going to have to take out all that material as it falls," Andres Sougarret, Codelco's head engineer on the operation, told The Associated Press Sunday in a phone interview.In all, the trapped miners will have to clear between 3,000 and 4,000 tons of rock, work that will require crews of about a half-dozen men working in shifts 24 hours a day.Sougarret declined to estimate how long the work would take, saying it would depend on how each step went.On Sunday, Mining Minister Laurence Golborne reiterated the government's estimate of three to four months to rescue the men, rejecting local reports citing engineers who said it could be done in much less time.Golborne said that experts had analyzed 10 different methods to get the men out, will continue to study other options, but that "nothing has yet been found that will be quicker."From the moment the mine collapsed, the trapped men have had a central role in keeping themselves alive — getting to the safety chamber, rationing food and keeping order with extraordinary discipline.