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C. DZY Loves Colors

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputDZY loves colors, and he enjoys painting.

On a colorful day, DZY gets a colorful ribbon, which consists of *n* units (they are numbered from 1 to *n* from left to right). The color of the *i*-th unit of the ribbon is *i* at first. It is colorful enough, but we still consider that the colorfulness of each unit is 0 at first.

DZY loves painting, we know. He takes up a paintbrush with color *x* and uses it to draw a line on the ribbon. In such a case some contiguous units are painted. Imagine that the color of unit *i* currently is *y*. When it is painted by this paintbrush, the color of the unit becomes *x*, and the colorfulness of the unit increases by |*x* - *y*|.

DZY wants to perform *m* operations, each operation can be one of the following:

- Paint all the units with numbers between
*l*and*r*(both inclusive) with color*x*. - Ask the sum of colorfulness of the units between
*l*and*r*(both inclusive).

Can you help DZY?

Input

The first line contains two space-separated integers *n*, *m* (1 ≤ *n*, *m* ≤ 10^{5}).

Each of the next *m* lines begins with a integer *type* (1 ≤ *type* ≤ 2), which represents the type of this operation.

If *type* = 1, there will be 3 more integers *l*, *r*, *x* (1 ≤ *l* ≤ *r* ≤ *n*; 1 ≤ *x* ≤ 10^{8}) in this line, describing an operation 1.

If *type* = 2, there will be 2 more integers *l*, *r* (1 ≤ *l* ≤ *r* ≤ *n*) in this line, describing an operation 2.

Output

For each operation 2, print a line containing the answer — sum of colorfulness.

Examples

Input

3 3

1 1 2 4

1 2 3 5

2 1 3

Output

8

Input

3 4

1 1 3 4

2 1 1

2 2 2

2 3 3

Output

3

2

1

Input

10 6

1 1 5 3

1 2 7 9

1 10 10 11

1 3 8 12

1 1 10 3

2 1 10

Output

129

Note

In the first sample, the color of each unit is initially [1, 2, 3], and the colorfulness is [0, 0, 0].

After the first operation, colors become [4, 4, 3], colorfulness become [3, 2, 0].

After the second operation, colors become [4, 5, 5], colorfulness become [3, 3, 2].

So the answer to the only operation of type 2 is 8.

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