B"Polycarp lives on a coordinate line at the point x = 0 . He goes to his friend that lives at the point x = a . Polycarp can move only from left to right, he can pass one unit of length each second. Now it's raining, so some segments of his way are in the rain. Formally, it's raining on n non-intersecting segments, the i -th segment which is in the rain is represented as [l_i, r_i] ( 0 <= l_i < r_i <= a ). There are m umbrellas lying on the line, the i -th umbrella is located at point x_i ( 0 <= x_i <= a ) and has weight p_i . When Polycarp begins his journey, he doesn't have any umbrellas. During his journey from x = 0 to x = a Polycarp can pick up and throw away umbrellas. Polycarp picks up and throws down any umbrella instantly. He can carry any number of umbrellas at any moment of time. Because Polycarp doesn't want to get wet, he must carry at least one umbrella while he moves from x to x + 1 if a segment [x, x + 1] is in the rain (i.e. if there exists some i such that l_i <= x and x + 1 <= r_i ). The condition above is the only requirement. For example, it is possible to go without any umbrellas to a point where some rain segment starts, pick up an umbrella at this point and move along with an umbrella. Polycarp can swap umbrellas while he is in the rain. Each unit of length passed increases Polycarp's fatigue by the sum of the weights of umbrellas he carries while moving. Can Polycarp make his way from point x = 0 to point x = a ? If yes, find the minimum total fatigue after reaching x = a , if Polycarp picks up and throws away umbrellas optimally. The first line contains three integers a , n and m ( 1 <= a, m <= 2000, 1 <= n <= lceil frac{a}{2} rceil ) -- the point at which Polycarp's friend lives, the number of the segments in the rain and the number of umbrellas. Each of the next n lines con"...