int twoRobots(int M, int N, vector<vector<int>> queries) {
    vector<vector<int>> cache(N, vector<int>(M+1, INT_MAX));
    set<int> endStates = {0};
    cache[0][0] = abs(queries[0][1] - queries[0][0]);
    for (int i=1; i < N; i++) {
        for (int x : endStates) cache[i][x] = cache[i-1][x] + abs(queries[i][0] - queries[i-1][1]) + abs(queries[i][1] - queries[i][0]);
        int temp = INT_MAX;
        for (int y : endStates) {
            if (y != 0) temp = min(temp, cache[i-1][y] + abs(queries[i][0] - y) + abs(queries[i][1] - queries[i][0]));
            else temp = min(temp, cache[i-1][y] + abs(queries[i][1] - queries[i][0]));
        }
        cache[i][queries[i-1][1]] = min(cache[i][queries[i-1][1]], temp);
        endStates.insert(queries[i-1][1]);
    }
    return *min_element(cache[N-1].begin(), cache[N-1].end());
}

inp = [[5,4],[1,5], [3,2], [4,1], [2,4], [4,2], [1,2], [4,3], [10,3],[2,4], [5,4], [9,8]]
print(two_robots(3,inp))

def two_robots(m,queries):
    i = 0

    def min_dist(queries):

        n = len(queries)
        i = 1
        R1, R2 = queries[0], None
        D1, D2 = abs(queries[0][1]-queries[0][0]), 0

        while ((R2 is None) and (i< n-1)):
            if abs(queries[i][0] - R1[1]) > abs(queries[i+1][0] - R1[1]):
                R2 = queries[i]
                D2+= abs(R2[0] - R2[1])
            else:
                D1+= abs(R1[1]- queries[i][0]) + abs(queries[i][0] - queries[i][1])
                R1 = queries[i]
            i = i+1
        if R2 is None:
            R2 = queries[i]
            D2+= abs(R2[0] - R2[1])
        else:
            while (i < n):
                if abs(queries[i][0]- R1[1]) > abs(queries[i][0] - R2[1]):
                    D2+= abs(R2[1]- queries[i][0]) + abs(queries[i][0] - queries[i][1])
                    R2 = queries[i]
                else:
                    D1+= abs(R1[1]- queries[i][0]) + abs(queries[i][0] - queries[i][1])
                    R1 = queries[i]
                i = i+1
        return D1+D2

    resultats = ""
    while i < m:
        n_cut = queries[0][1]
        res = min_dist(queries[1:n_cut+1])
        resultats = resultats + str(res) + "\n"
        queries = queries[n_cut+1:]
        i = i+1
    return resultats