Mutual Table Partners

There are \(2n\) children in a class, numbered \(1, 2, \ldots, 2n\). The classroom has \(n\) tables and each table seats exactly two children. If two children sit at the same table, they are table partners. A child cannot be paired with him/herself.

Each child \(i\) expresses his/her desire to sit with child \(p_i\). Help the teacher determine if it is possible to assign the seats so that every child gets to sit with his/her desired partner.

Note: In order for every child to be satisfied, the pairing must be mutual, that is, for every \(i\) the condition \(p_{p_i} = i\) must hold.

inputFormat

The first line contains a single integer \(n\) representing the number of tables. The second line contains \(2n\) integers \(p_1, p_2, \ldots, p_{2n}\), where \(p_i\) indicates the child that child \(i\) wishes to sit with.

It is guaranteed that \(p_i \neq i\) for all \(i

outputFormat

Output a single line containing YES if it is possible to seat the children so that every child sits with his/her desired partner, and NO otherwise.

sample

2
2 1 4 3

YES