B"You are responsible for installing a gas pipeline along a road. Let's consider the road (for simplicity) as a segment [0, n] on OX axis. The road can have several crossroads, but for simplicity, we'll denote each crossroad as an interval (x, x + 1) with integer x . So we can represent the road as a binary string consisting of n characters, where character 0 means that current interval doesn't contain a crossroad, and 1 means that there is a crossroad. Usually, we can install the pipeline along the road on height of 1 unit with supporting pillars in each integer point (so, if we are responsible for [0, n] road, we must install n + 1 pillars). But on crossroads we should lift the pipeline up to the height 2 , so the pipeline won't obstruct the way for cars. We can do so inserting several zig-zag-like lines. Each zig-zag can be represented as a segment [x, x + 1] with integer x consisting of three parts: 0.5 units of horizontal pipe + 1 unit of vertical pipe + 0.5 of horizontal. Note that if pipeline is currently on height 2 , the pillars that support it should also have length equal to 2 units. Each unit of gas pipeline costs us a bourles, and each unit of pillar -- b bourles. So, it's not always optimal to make the whole pipeline on the height 2 . Find the shape of the pipeline with minimum possible cost and calculate that cost. Note that you must start and finish the pipeline on height 1 and, also, it's guaranteed that the first and last characters of the input string are equal to 0. The fist line contains one integer T ( 1 <= T <= 100 ) -- the number of queries. Next 2 cdot T lines contain independent queries -- one query per two lines. The first line contains three integers n , a , b ( 2 <= n <= 2 cdot 10^5 , 1 <= a <= 10^8 , 1 <= b <= 10^8 ) -- the length of the road, the cost of "...