The Thought Police (TP) is trying to dismantle a network of thought-criminals (TC). As it may be easily inferred from the name, TCs commit thought-crimes and they do so by sending messages through a communication network that TCs believe to be secure, but which has already been infiltrated by the TP. In order to preserve the security of the communication network, each TC only communicates with a reduced set of contacts, so a message may need to go through several intermediate TCs to reach its destination. The TCs in the communication network are connected in such a way that a message from any source may reach any destination. Even though the TP knows all the TCs of the network, they want to interrupt its activity in the most subtle way. The plan is to identify the weak links of the network. A weak link is any single link that if removed, would make it impossible for at least one TC to communicate with some other TC in the network. For instance, the next figure shows a network with 7 TCs. The connection between TCs 3 and 4 is a weak link since, if removed, it would make it impossible for TCs 0,1,2,3 to communicate with TCs 4,5,6. All the other connections of the network are not weak links. The government has hired you to support its crusade to defend the country from thought-criminals and to preserve the security of its citizens, by helping the TP to carry on its plan identifying the weak links of the TCs communication network. Input The input contains several test cases. The first line of each test case contains two blank-separated integers n and m, where n is the number of TCs (2 ≤ n ≤ 1000), and m is the number of direct communications links between them (1 ≤ m ≤ 10000). Then m lines follow, each one containing two blank-separated integers Ni and Nj (0 ≤ Ni < Nj < n), indicating that there is a direct communication link between TCs Ni and Nj in the communication network. Note that all communication links are bidirectional. A line with two zeros ‘0 0’ indicates the end of the input. Output For each test case, a line with the list of the weak links has to be printed. Each line starts with a number p indicating the number of weak links in the communication network, then p links of the form Nik Njk must follow (0 ≤ Nik < Njk < n). Weak links must be printed in ascending order of their Nik . If two weak links have the same Nik , the link with the minimum Njk should be printed before. All numbers printed in each line should be separated by a single blank. There are no blanks after the last number of any line.
2/2 Sample Input 43 03 01 02 78 01 02 13 23 34 45 46 56 00 Sample Output 3010203 134