HelpWTck:=proc(): print(`WhatTypeG(pi) `): end:

reverse:=proc(L,i,j) local n,k:
 n:=nops(L):
 [op(1..i-1, L), seq(L[n-k], k = n-j .. n-i), op(j+1..n, L)]:
end:

posi:=proc(pi,a) local i:
 for i from 1 to nops(pi) do
  if pi[i]=a then return i:  fi:
 od:
 return FAIL:
end:

SRS:=proc(pi) local i,j,n,L,Id,L1:
 n:=nops(pi):
 L:=pi:
 L1:=[]:
 Id:=[seq(i,i=1..n)]:
 for i from 1 to n-1 do
  j:=posi(L,i):
  if j<>i then
   L:=reverse(L,i,j):
   L1:=[op(L1),[i,j]]:
  fi:
  if L=Id then
   return L,L1:
  fi:
 od:
 return L,L1:
end:

b:=proc(pi) local i,n:
 n:=0:
 for i from 1 to nops(pi)-1 do
  if abs(pi[i+1]-pi[i])<>1 then
   n:=n+1:
  fi:
 od:
 return n:
end:

BRS:=proc(pi) local L,n,i,j,min,s,L1:
 n:=nops(pi):
 L1:=[]:
 L:=[0,op(pi),n+1]:
 while b(L)>0 do
  min:=n:
  for i from 2 to n do
   for j from i+1 to n+1 do
    if b(reverse(L,i,j))<min then
     min:=b(reverse(L,i,j)):
     s:=[i,j]:
    fi:
   od:
  od:
  L:=reverse(L,s[1],s[2]):
  L1:=[op(L1),[s[1]-1,s[2]-1]]:
 od:
 [op(2..n+1,L)],L1:
end:

Strip:=proc(pi) local L,i,j:
 L:=BD(pi):
 for i from 1 to nops(L) do
  if nops(L[i])>1 then
   if L[i][2]-L[i][1]=-1 then
    return 1:
   fi:
  fi:
 od:
 for i from 1 to nops(L) do
  if nops(L[i])>1 then
   if L[i][2]-L[i][1]=1 then
    return [add(nops(L[j]),j=1..i-1)+1,add(nops(L[j]),j=1..i)]:
   fi:
  fi:
 od:
 return 1:
end:

IBRS:=proc(pi) local L,n,i,j,min,s,L1:
 n:=nops(pi):
 L1:=[]:
 L:=[0,op(pi),n+1]:
 while b(L)>0 do
  min:=n:
  if Strip(L)=1 then
   for i from 2 to n do
    for j from i+1 to n+1 do
     if b(reverse(L,i,j))<min then
      min:=b(reverse(L,i,j)):
      s:=[i,j]:
     fi:
    od:
   od:
  else 
   s:=Strip(L):
  fi:
  L:=reverse(L,s[1],s[2]):
  L1:=[op(L1),[s[1]-1,s[2]-1]]:
 od:
 [op(2..n+1,L)],L1:
end:

WhatTypeG:=proc(pi) local M,M1,m1,l1,l2,L,L1,i:



 M:=BD(pi):
 L1:=[]:
 M1:=max(M[1])+1:
 m1:=min(M[1])-1:
 l1:=FindBlock(M,M1):
 l2:=FindBlock(M,m1):
 if nops(M)=1 then
  return [[0,SimaoHerdade(M[1])]],[nops(pi)]:
 fi:
 if l1=FAIL then 
  if l2=2 then
   L:=[[0,SimaoHerdade(M[1])],[-1,SimaoHerdade(M[l2])]]:
   L1:=[nops(M[1]),nops(M[1])+nops(M[2])]:
  else
   L:=[[0,SimaoHerdade(M[1])],0,[-1,SimaoHerdade(M[l2])]]:
   L1:=[nops(M[1]),add(nops(M[i]),i=1..l2-1),add(nops(M[i]),i=1..l2)]:
  fi:
  if l2<>nops(M) then
   L:=[op(L),0]:
   L1:=[op(L1),nops(pi)]:
  fi:
 elif l2=FAIL then
  if l1=2 then
   L:=[[0,SimaoHerdade(M[1])],[1,SimaoHerdade(M[l1])]]:
   L1:=[nops(M[1]),nops(M[1])+nops(M[2])]:
  else
   L:=[[0,SimaoHerdade(M[1])],0,[1,SimaoHerdade(M[l1])]]:
   L1:=[nops(M[1]),add(nops(M[i]),i=1..l1-1),add(nops(M[i]),i=1..l1)]:
  fi:
  if l1<>nops(M) then
   L:=[op(L),0]:
   L1:=[op(L1),nops(pi)]:
  fi: 
 elif l1>l2 then
  if l2=2 then
   L:=[[0,SimaoHerdade(M[1])],[-1,SimaoHerdade(M[l2])]]:
   L1:=[nops(M[1]),nops(M[1])+nops(M[2])]:
  else
   L:=[[0,SimaoHerdade(M[1])],0,[-1,SimaoHerdade(M[l2])]]:
   L1:=[nops(M[1]),add(nops(M[i]),i=1..l2-1),add(nops(M[i]),i=1..l2)]:
  fi:
  if l1-l2=1 then
   L:=[op(L),[1,SimaoHerdade(M[l1])]]:
   L1:=[op(L1),add(nops(M[i]),i=1..l1)]:
  else
   L:=[op(L),0,[1,SimaoHerdade(M[l1])]]:
   L1:=[op(L1),add(nops(M[i]),i=1..l1-1),add(nops(M[i]),i=1..l1)]:
  fi:
  if l1<>nops(M) then
   L:=[op(L),0]:
   L1:=[op(L1),nops(pi)]:
  fi:
 else
  if l1=2 then
   L:=[[0,SimaoHerdade(M[1])],[1,SimaoHerdade(M[l1])]]:
   L1:=[nops(M[1]),nops(M[1])+nops(M[2])]:
  else
   L:=[[0,SimaoHerdade(M[1])],0,[1,SimaoHerdade(M[l1])]]:
   L1:=[nops(M[1]),add(nops(M[i]),i=1..l1-1),add(nops(M[i]),i=1..l1)]:
  fi:
  if l2-l1=1 then
   L:=[op(L),[-1,SimaoHerdade(M[l2])]]:
   L1:=[op(L1),add(nops(M[i]),i=1..l2)]:
  else
   L:=[op(L),0,[-1,SimaoHerdade(M[l2])]]:
   L1:=[op(L1),add(nops(M[i]),i=1..l2-1),add(nops(M[i]),i=1..l2)]:
  fi:
  if l2<>nops(M) then
   L:=[op(L),0]:
   L1:=[op(L1),nops(pi)]:
  fi:
 fi:
 return L,L1:
end: