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E. Yaroslav and Points

time limit per test

5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYaroslav has *n* points that lie on the *Ox* axis. The coordinate of the first point is *x*_{1}, the coordinate of the second point is *x*_{2}, ..., the coordinate of the *n*-th point is — *x*_{n}. Now Yaroslav wants to execute *m* queries, each of them is of one of the two following types:

- Move the
*p*_{j}-th point from position*x*_{pj}to position*x*_{pj}+*d*_{j}. At that, it is guaranteed that after executing such query all coordinates of the points will be distinct. - Count the sum of distances between all pairs of points that lie on the segment [
*l*_{j},*r*_{j}] (*l*_{j}≤*r*_{j}). In other words, you should count the sum of: .

Help Yaroslav.

Input

The first line contains integer *n* — the number of points (1 ≤ *n* ≤ 10^{5}). The second line contains distinct integers *x*_{1}, *x*_{2}, ..., *x*_{n} — the coordinates of points (|*x*_{i}| ≤ 10^{9}).

The third line contains integer *m* — the number of queries (1 ≤ *m* ≤ 10^{5}). The next *m* lines contain the queries. The *j*-th line first contains integer *t*_{j} (1 ≤ *t*_{j} ≤ 2) — the query type. If *t*_{j} = 1, then it is followed by two integers *p*_{j} and *d*_{j} (1 ≤ *p*_{j} ≤ *n*, |*d*_{j}| ≤ 1000). If *t*_{j} = 2, then it is followed by two integers *l*_{j} and *r*_{j} ( - 10^{9} ≤ *l*_{j} ≤ *r*_{j} ≤ 10^{9}).

It is guaranteed that at any moment all the points have distinct coordinates.

Output

For each type 2 query print the answer on a single line. Print the answers in the order, in which the queries follow in the input.

Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams of the %I64d specifier.

Examples

Input

8

36 50 28 -75 40 -60 -95 -48

20

2 -61 29

1 5 -53

1 1 429

1 5 130

2 -101 -71

2 -69 53

1 1 404

1 5 518

2 -101 53

2 50 872

1 1 -207

2 -99 -40

1 7 -389

1 6 -171

1 2 464

1 7 -707

1 1 -730

1 1 560

2 635 644

1 7 -677

Output

176

20

406

1046

1638

156

0

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