Bangkok (CNN) Navy divers are searching a flooded cave for 12 missing boys in northern Thailand, three days after they're believed to have ventured inside with their soccer coach.

As search teams pushed deeper into Tham Luang Nang Non Cave in Chiang Rai on Tuesday, hopes remained high that the boys and their coach would survive the ordeal.

"We are still optimistic they are all alive," Deputy Prime Minister Prawit Wongsuwon told the Bangkok Post . "Even though they may not have anything to eat, they should have water to drink."

Officials believe the local soccer team crawled into the cave through a narrow 15-meter long channel, leading to a series of caves up to three kilometers (1.86 miles) long.

Rising waters then blocked the path, which is about as wide as a single person, leaving the group stuck inside the cave network, Kamolchai Kotcha, an official with Thailand's national parks authority, told CNN on Monday.

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