The captain and his three sailors get 2009 golden coins with the same value . The four people decided to divide these coins by the following rules : sailor 1,sailor 2,sailor 3 everyone write down an integer b1,b2,b3 , satisfies b1≥b2≥b3 , and b1+b2+b3=2009; the captain dosen't know what the numbers the sailors have written . He divides 2009 coins into 3 piles , with number of coins: a1,a2,a3 , and a1≥a2≥a3 . For sailor k (k=1,2,3) , if bk<ak , then he can take bk coins from the kth pile ; if bk≥ak , then he can't take any coins away . At last , the captain own the rest of the coins .If no matter what the numbers the sailors write , the captain can make sure that he always gets n coins . Find the largest possible value of n and prove your conclusion .