Shave Beaver!
Description
The Smart Beaver has recently designed and built an innovative nanotechnologic all-purpose beaver mass shaving machine, "Beavershave 5000". Beavershave 5000 can shave beavers by families! How does it work? Very easily!
There are n beavers, each of them has a unique id from 1 to n. Consider a permutation a1, a2, ..., an of n these beavers. Beavershave 5000 needs one session to shave beavers with ids from x to y (inclusive) if and only if there are such indices i1 < i2 < ... < ik, that ai1 = x, ai2 = x + 1, ..., aik - 1 = y - 1, aik = y. And that is really convenient. For example, it needs one session to shave a permutation of beavers 1, 2, 3, ..., n.
If we can't shave beavers from x to y in one session, then we can split these beavers into groups [x, p1], [p1 + 1, p2], ..., [pm + 1, y] (x ≤ p1 < p2 < ... < pm < y), in such a way that the machine can shave beavers in each group in one session. But then Beavershave 5000 needs m + 1 working sessions to shave beavers from x to y.
All beavers are restless and they keep trying to swap. So if we consider the problem more formally, we can consider queries of two types:
- what is the minimum number of sessions that Beavershave 5000 needs to shave beavers with ids from x to y, inclusive?
- two beavers on positions x and y (the beavers ax and ay) swapped.
You can assume that any beaver can be shaved any number of times.
The first line contains integer n — the total number of beavers, 2 ≤ n. The second line contains n space-separated integers — the initial beaver permutation.
The third line contains integer q — the number of queries, 1 ≤ q ≤ 105. The next q lines contain the queries. Each query i looks as pi xi yi, where pi is the query type (1 is to shave beavers from xi to yi, inclusive, 2 is to swap beavers on positions xi and yi). All queries meet the condition: 1 ≤ xi < yi ≤ n.
- to get 30 points, you need to solve the problem with constraints: n ≤ 100 (subproblem B1);
- to get 100 points, you need to solve the problem with constraints: n ≤ 3·105 (subproblems B1+B2).
Note that the number of queries q is limited 1 ≤ q ≤ 105 in both subproblem B1 and subproblem B2.
For each query with pi = 1, print the minimum number of Beavershave 5000 sessions.
Input
The first line contains integer n — the total number of beavers, 2 ≤ n. The second line contains n space-separated integers — the initial beaver permutation.
The third line contains integer q — the number of queries, 1 ≤ q ≤ 105. The next q lines contain the queries. Each query i looks as pi xi yi, where pi is the query type (1 is to shave beavers from xi to yi, inclusive, 2 is to swap beavers on positions xi and yi). All queries meet the condition: 1 ≤ xi < yi ≤ n.
- to get 30 points, you need to solve the problem with constraints: n ≤ 100 (subproblem B1);
- to get 100 points, you need to solve the problem with constraints: n ≤ 3·105 (subproblems B1+B2).
Note that the number of queries q is limited 1 ≤ q ≤ 105 in both subproblem B1 and subproblem B2.
Output
For each query with pi = 1, print the minimum number of Beavershave 5000 sessions.
Samples
5
1 3 4 2 5
6
1 1 5
1 3 4
2 2 3
1 1 5
2 1 5
1 1 5
2
1
3
5