John Doe decided that some mathematical object must be named after him. So he invented the Doe graphs. The Doe graphs are a family of undirected graphs, each of them is characterized by a single non-negative number − its order.

We'll denote a graph of order k as D(k), and we'll denote the number of vertices in the graph D(k) as |D(k)|. Then let's define the Doe graphs as follows:

• D(0) consists of a single vertex, that has number 1.
• D(1) consists of two vertices with numbers 1 and 2, connected by an edge.
• D(n) for n≥2 is obtained from graphs D(n-1) and D(n-2). D(n-1) and D(n-2) are joined in one graph, at that numbers of all vertices of graph D(n-2) increase by |D(n-1)| (for example, vertex number 1 of graph D(n-2) becomes vertex number 1+|D(n-1)|). After that two edges are added to the graph: the first one goes between vertices with numbers |D(n-1)| and |D(n-1)|+1, the second one goes between vertices with numbers |D(n-1)|+1 and 1. Note that the definition of graph D(n) implies, that D(n) is a connected graph, its vertices are numbered from 1 to |D(n)|.

The picture shows the Doe graphs of order 1, 2, 3 and 4, from left to right.

John thinks that Doe graphs are that great because for them exists a polynomial algorithm for the search of Hamiltonian path. However, your task is to answer queries of finding the shortest-length path between the vertices a_i and b_i in the graph D(n).

A path between a pair of vertices u and v in the graph is a sequence of vertices x₁, x₂, ..., x_k (k>1) such, that x₁=u, x_k=v, and for any i (i<k) vertices x_i and x_i+1 are connected by a graph edge. The length of path x₁, x₂, ..., x_k is number (k-1).