# Homo or Hetero?

# Homo or Hetero?

Consider a list of numbers with two operations:

*insert number*— adds the specified number to the end of the list.*delete number*— removes the first occurrence of the specified number from the list. If the list does not contain the number specified, no changes are performed.

For example: the result of the insertion of a number 4 to the list [1,2,1] is the list [1,2,1,4]. If we delete the number 1 from this list, we get the list [2,1,4], but if we delete the number 3 from the list [1,2,1,4],the list stays unchanged.

The list is *homogeneous* if it contains at least two equal numbers and the list is *heterogeneous* if it contains at least two different numbers. For example: the list [2,2] is homogeneous, the list [2,1,4] is heterogeneous, the list [1,2,1,4] is both, and the empty list is neither homogeneous, nor heterogeneous.

Write a program that handles a number of the operations insert and delete on the empty list and determines list’s homogeneity and heterogeneity after each operation.

#### Input

The first line of the input file contains an integer number `N`

(`1 ≤ N ≤ 10`

) — the number of operations to handle. Following N lines contain one operation description each. The operation description consists of a word “insert” or “delete”, followed by an integer number ^{5}`K`

(`-10`

) — the operation argument.^{9} ≤ K ≤ 10^{9}

#### Output

For each operation output a line, containing a single word, describing the state of the list after the operation:

- “both” — if the list is both homogeneous and heterogeneous.
- “homo” — if the list is homogeneous, but not heterogeneous.
- “hetero” — if the list is heterogeneous, but not homogeneous.
- “neither” — if the list is neither homogeneous nor heterogeneous.

11 insert 1 insert 2 insert 1 insert 4 delete 1 delete 3 delete 2 delete 1 insert 4 delete 4 delete 4

neither hetero both both hetero hetero hetero neither homo neither neither