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1470. UFOs

Time limit: 2.0 second
Memory limit: 64 MB
Vasya is a ufologist and his duties include observing Unidentified Flying Objects (UFOs) in the part of space bounded by a cube N × N × N. The cube is divided into cubic sectors 1 × 1 × 1. During the observation, the following events may happen:
• several new UFOs emerge in a certain sector;
• several UFOs disappear in a certain sector;
• Vasya's boss may ask him how many UFOs there are in a part of space consisting of several sectors.
At the moment when Vasya starts his observations there are no UFOs in the whole space.

Input

The first line contains an integer N (1 ≤ N ≤ 128). The coordinates of sectors are integers from 0 to N–1.
Then there are entries describing events, one entry per line. Each entry starts with a number M.
• If M is 1, then this number is followed by four integers x (0 ≤ x < N), y (0 ≤ y < N), z (0 ≤ z < N), K (–20000 ≤ K ≤ 20000), which are coordinates of a sector and the change in the number of UFOs in this sector. The number of UFOs in a sector cannot become negative.
• If M is 2, then this number is followed by six integers x1, y1, z1, x2, y2, z2 (0 ≤ x1x2 < N, 0 ≤ y1y2 < N, 0 ≤ z1z2 < N), which mean that Vasya must compute the total number of UFOs in sectors (x, y, z) belonging to the volume: x1xx2, y1yy2, z1zz2.
• If M is 3, it means that Vasya is tired and goes to sleep. This entry is always the last one.
The number of entries does not exceed 100002.

Output

For each query, output in a separate line the required number of UFOs.

Sample

inputoutput
```2
2 1 1 1 1 1 1
1 0 0 0 1
1 0 1 0 3
2 0 0 0 0 0 0
2 0 0 0 0 1 0
1 0 1 0 -2
2 0 0 0 1 1 1
3
```
```0
1
4
2
```
Problem Author: Dmitry Zhukov
Problem Source: Ural SU and Orel STU Contest. Petrozavodsk Summer Session, August 2006