Four refugees are stranded on an island and must reach the safety of a distant shore. They have only one raft, and the waters are too dangerous to swim across the channel without it. The current flows strongly toward the island, so it requires two refugees paddling together to have enough strength to make it to the shore. The raft can carry at most two refugees at a time, and when they paddle together, they travel at the slower refugee's pace. The four refugees paddle at different speeds: one can reach the shore in 1 minute, another in 2 minutes, another in 5 minutes, and the slowest takes 10 minutes. What is the fastest time all the refugees can reach the shore?