The fact that the range of the mapping applied to the Dyck words of length, 4, equals the set Gn(i) with i=, 1, is true The fact that the range of the mapping applied to the Dyck words of length, 6, equals the set Gn(i) with i=, 2, is true The fact that the range of the mapping applied to the Dyck words of length, 8, equals the set Gn(i) with i=, 3, is true The fact that the range of the mapping applied to the Dyck words of length, 10, equals the set Gn(i) with i=, 4, is true The fact that the range of the mapping applied to the Dyck words of length, 12, equals the set Gn(i) with i=, 5, is true The fact that the range of the mapping applied to the Dyck words of length, 14, equals the set Gn(i) with i=, 6, is true The fact that the range of the mapping applied to the Dyck words of length, 16, equals the set Gn(i) with i=, 7, is true The fact that the range of the mapping applied to the Dyck words of length, 18, equals the set Gn(i) with i=, 8, is true The fact that the range of the mapping applied to the Dyck words of length, 20, equals the set Gn(i) with i=, 9, is true The fact that the range of the inverse mapping applied to the set Gn(i) with\ i=, 1, is Cn(i+1) with that i true The fact that the range of the inverse mapping applied to the set Gn(i) with\ i=, 2, is Cn(i+1) with that i true The fact that the range of the inverse mapping applied to the set Gn(i) with\ i=, 3, is Cn(i+1) with that i true The fact that the range of the inverse mapping applied to the set Gn(i) with\ i=, 4, is Cn(i+1) with that i true The fact that the range of the inverse mapping applied to the set Gn(i) with\ i=, 5, is Cn(i+1) with that i true The fact that the range of the inverse mapping applied to the set Gn(i) with\ i=, 6, is Cn(i+1) with that i true The fact that the range of the inverse mapping applied to the set Gn(i) with\ i=, 7, is Cn(i+1) with that i true The fact that the range of the inverse mapping applied to the set Gn(i) with\ i=, 8, is Cn(i+1) with that i true The fact that the range of the inverse mapping applied to the set Gn(i) with\ i=, 9, is Cn(i+1) with that i true The fact that the composition of the map and its alleged inverse is the ide\ ntity map is true The fact that the composition of the map and its alleged inverse is the ide\ ntity map is true The fact that the composition of the map and its alleged inverse is the ide\ ntity map is true The fact that the composition of the map and its alleged inverse is the ide\ ntity map is true The fact that the composition of the map and its alleged inverse is the ide\ ntity map is true The fact that the composition of the map and its alleged inverse is the ide\ ntity map is true The fact that the composition of the map and its alleged inverse is the ide\ ntity map is true The fact that the composition of the map and its alleged inverse is the ide\ ntity map is true The fact that the composition of the map and its alleged inverse is the ide\ ntity map is true The fact that the composition of the alleged inverse map with the map is th\ e identity map is true The fact that the composition of the alleged inverse map with the map is th\ e identity map is true The fact that the composition of the alleged inverse map with the map is th\ e identity map is true The fact that the composition of the alleged inverse map with the map is th\ e identity map is true The fact that the composition of the alleged inverse map with the map is th\ e identity map is true The fact that the composition of the alleged inverse map with the map is th\ e identity map is true The fact that the composition of the alleged inverse map with the map is th\ e identity map is true The fact that the composition of the alleged inverse map with the map is th\ e identity map is true The fact that the composition of the alleged inverse map with the map is th\ e identity map is true The whole thing took, 5.933, seconds.