You will be given a list of n integers S = {1, 2, ... , (n-1), n}, please write a program to calculate the minimum number of instructions required to change the list in descending order {n, (n-1), ..., 1}. Let S[i] denote the i-th element of S, 1 ≤ i ≤ n.

Each instruction takes a successive subsequence and removes that subsequence from the list, then insert that subsequence into any position of the list as a parameter. Each instruction can be represented by three numbers (pos₁,length,pos₂)，which means we will remove subsequence S[pos₁] ..... S[pos₁+length-1], then insert them after the S[pos₂] (pos₂=0 will insert it at the beginning). We always have: 1 ≤ pos₁ ≤ n, 1 ≤ length ≤ n+1-pos₁, 0 ≤ pos₂ ≤ n-length

For example:
The list S = {4,6,5,3,1,2}，instruction (2,3,0) to get {6,5,3,4,1,2}
The list S = {4,6,5,3,1,2}，instruction (3,1,2) to get {4,6,5,3,1,2}
The list S = {4,6,5,3,1,2}，instruction (4,3,1) to get {4,3,1,2,6,5}
The list S = {4,6,5,3,1,2}，instruction (2,4,2) to get {4,2,6,5,3,1}