The city council in the town of Durburn has decided to improve road sign placement, especially for the numerous dead ends that are currently unmarked in various parts of the city. They have given you a road map, and you must determine where to put up signs to mark all the dead ends. They want you to use as few signs as possible.
The road map is a collection of locations connected by two-way streets.
The following rule describes how to obtain a complete placement of dead-end signs:
Consider a street S connecting a location x with another location. The x-entrance of S gets a dead-end sign if, after entering S from x, it is not possible to come back to x without making a U-turn. A U-turn is a 180- degree turn immediately reversing the direction.
To save costs, you have decided that you won’t install redundant dead-end signs, as specified by the following rule:
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Consider a street S with a dead-end sign at its x-entrance and another street T with a dead-end sign at its y-entrance. If, after entering S from x, it is possible to go to y and enter T without making a U-turn, the dead-end sign at the y-entrance of T is redundant. INPUT
The first line of input contains two integers n and m, where n (1 ≤ n ≤ 5*105) is the number of locations and m (0 ≤ m ≤5 * 105) is the number of streets. Each of the following m lines contains two integers v and w (1 ≤ v < w ≤ n) indicating that there is a two-way street connecting locations v and w. All location pairs in the input are distinct. OUTPUT On the first line, output k, the number of dead-end signs installed. On each of the next k lines, output two integers v and w marking that a dead-end sign should be installed at the v-entrance of a street connecting locations v and w. The lines describing dead-end signs must be sorted in ascending order of v-locations, breaking ties in ascending order of w-locations
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