CF855F.Nagini

Nagini, being a horcrux You-know-who created with the murder of Bertha Jorkins, has accumulated its army of snakes and is launching an attack on Hogwarts school.

Hogwarts' entrance can be imagined as a straight line (x-axis) from 1 to 105. Nagini is launching various snakes at the Hogwarts entrance. Each snake lands parallel to the entrance, covering a segment at a distance k from x = l to x = r. Formally, each snake can be imagined as being a line segment between points (l, k) and (r, k). Note that k can be both positive and negative, but not 0.

Let, at some x-coordinate x = i, there be snakes at point (i, _y_1) and point (i, _y_2), such that _y_1 > 0 and _y_2 < 0. Then, if for any point (i, _y_3) containing a snake such that _y_3 > 0, _y_1 ≤ _y_3 holds and for any point (i, _y_4) containing a snake such that _y_4 < 0, |_y_2| ≤ |_y_4| holds, then the danger value at coordinate x = i is _y_1 + |_y_2|. If no such _y_1 and _y_2 exist, danger value is 0.

Harry wants to calculate the danger value of various segments of the Hogwarts entrance. Danger value for a segment [l, r) of the entrance can be calculated by taking the sum of danger values for each integer x-coordinate present in the segment.

Formally, you have to implement two types of queries:

• 1 l r k: a snake is added parallel to entrance from x = l to x = r at y-coordinate y = k (l inclusive, r exclusive).
• 2 l r: you have to calculate the danger value of segment l to r (l inclusive, r exclusive).

纳吉尼是伏地魔杀害伯莎·乔金斯后制造的魂器，它已集结起蛇群，正向霍格沃茨学校发起进攻。

霍格沃茨的入口可被建模为一条直线（即 $x$ 轴），范围从 $1$ 到 $10^5$。纳吉尼正向霍格沃茨入口投掷各类蛇。每条蛇以与入口平行的方式着陆，在距离 $x = l$ 到 $x = r$ 的区间上覆盖一段线段，其纵坐标为 $k$。形式化地说，每条蛇可视为连接点 $(l,\,k)$ 与 $(r,\,k)$ 的一条线段。注意：$k$ 可取正数或负数，但不能为 $0$。

设在某横坐标 $x = i$ 处，存在两条蛇分别位于点 $(i,\,y_1)$ 和 $(i,\,y_2)$，满足 $y_1 > 0$ 且 $y_2 < 0$。若对任意位于 $(i,\,y_3)$ 的蛇（其中 $y_3 > 0$）均有 $y_1 \le y_3$，且对任意位于 $(i,\,y_4)$ 的蛇（其中 $y_4 < 0$）均有 $|y_2| \le |y_4|$，则横坐标 $x = i$ 处的危险值为 $y_1 + |y_2|$。若不存在满足上述条件的 $y_1$ 和 $y_2$，则该坐标的危险值为 $0$。

哈利希望计算霍格沃茨入口若干区间的危险值。入口区间 $[l,\,r)$ 的危险值定义为该区间内所有整数横坐标 $x$ 对应的危险值之和。

形式化地，你需要支持以下两种操作：

• 1 l r k：添加一条蛇，其沿入口方向（即水平方向）覆盖横坐标区间 $[l,\,r)$（含 $l$，不含 $r$），纵坐标为 $y = k$；
• 2 l r：计算横坐标区间 $[l,\,r)$（含 $l$，不含 $r$）的危险值。

First line of input contains a single integer q (1 ≤ q ≤ 5·104) denoting the number of queries.

Next q lines each describe a query. Each query description first contains the query type type__i (1 ≤ type__i ≤ 2). This is followed by further description of the query. In case of the type being 1, it is followed by integers l__i, r__i and k__i (,  - 109 ≤ k__i ≤ 109, k ≠ 0). Otherwise, it just contains two integers, l__i and r__i (1 ≤ l__i < r__i ≤ 105).

输入的第一行包含一个整数 $ q $（$ 1 \leq q \leq 5 \cdot 10^4 $），表示查询次数。

接下来的 $ q $ 行每行描述一次查询。每次查询首先给出查询类型 $ \text{type}_i $（$ 1 \leq \text{type}_i \leq 2 $），随后是该查询的进一步描述。若查询类型为 1，则其后跟三个整数 $ l_i $、$ r_i $ 和 $ k_i $（，$ -10^9 \leq k_i \leq 10^9 $，且 $ k_i \neq 0 $）；否则（即查询类型为 2），仅包含两个整数 $ l_i $ 和 $ r_i $（$ 1 \leq l_i < r_i \leq 10^5 $）。

Output the answer for each query of type 2 in a separate line.

对每个类型为 2 的查询，分别在单独一行中输出答案。

In the first sample case, the danger value for x-coordinates 1 is 0 as there is no _y_2 satisfying the above condition for x = 1.

Danger values for x-coordinates 2 and 3 is 10 + | - 7| = 17.

Danger values for x-coordinates 4 to 9 is again 0 as there is no _y_2 satisfying the above condition for these coordinates.

Thus, total danger value is 17 + 17 = 34.

在第一个样例中，当 $x$ 坐标为 1 时，危险值为 0，因为对于 $x = 1$，不存在满足上述条件的 $y_2$。

当 $x$ 坐标为 2 和 3 时，危险值为 $10 + |-7| = 17$。

当 $x$ 坐标为 4 至 9 时，危险值再次为 0，因为对于这些坐标，不存在满足上述条件的 $y_2$。

因此，总危险值为 $17 + 17 = 34$。