題目2 : Total Highway Distance
時間限制:10000ms
單點時限:1000ms
記憶體限制:256MB
描述
Little Hi and Little Ho are playing a construction simulation game. They build N cities (numbered from 1 to N) in the game and connect them by N-1 highways. It is guaranteed that each pair of cities are connected by the highways directly or indirectly.

The game has a very important value called Total Highway Distance (THD) which is the total distances of all pairs of cities. Suppose there are 3 cities and 2 highways. The highway between City 1 and City 2 is 200 miles and the highway between City 2 and City 3 is 300 miles. So the THD is 1000(200 + 500 + 300) miles because the distances between City 1 and City 2, City 1 and City 3, City 2 and City 3 are 200 miles, 500 miles and 300 miles respectively.

During the game Little Hi and Little Ho may change the length of some highways. They want to know the latest THD. Can you help them?

輸入
Line 1: two integers N and M.

Line 2 .. N: three integers u, v, k indicating there is a highway of k miles between city u and city v.

Line N+1 .. N+M: each line describes an operation, either changing the length of a highway or querying the current THD. It is in one of the following format.

EDIT i j k, indicating change the length of the highway between city i and city j to k miles.

QUERY, for querying the THD.

For 30% of the data: 2<=N<=100, 1<=M<=20

For 60% of the data: 2<=N<=2000, 1<=M<=20

For 100% of the data: 2<=N<=100,000, 1<=M<=50,000, 1 <= u, v <= N, 0 <= k <= 1000.

輸出
For each QUERY operation output one line containing the corresponding THD.

樣例輸入
3 5
1 2 2
2 3 3
QUERY
EDIT 1 2 4
QUERY
EDIT 2 3 2
QUERY
樣例輸出
10
14
12

題目3 : Fibonacci
時間限制:10000ms
單點時限:1000ms
記憶體限制:256MB
描述
Given a sequence {an}, how many non-empty sub-sequence of it is a prefix of fibonacci sequence.

A sub-sequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.

The fibonacci sequence is defined as below:

F1 = 1, F2 = 1

Fn = Fn-1 + Fn-2, n>=3

輸入
One line with an integer n.

Second line with n integers, indicating the sequence {an}.

For 30% of the data, n<=10.

For 60% of the data, n<=1000.

For 100% of the data, n<=1000000, 0<=ai<=100000.

輸出
One line with an integer, indicating the answer modulo 1,000,000,007.

樣例提示
The 7 sub-sequences are:

{a2}

{a3}

{a2, a3}

{a2, a3, a4}

{a2, a3, a5}

{a2, a3, a4, a6}

{a2, a3, a5, a6}

樣例輸入
6
2 1 1 2 2 3
樣例輸出
7

題目4 : Image Encryption
時間限制:10000ms
單點時限:1000ms
記憶體限制:256MB
描述
A fancy square image encryption algorithm works as follow:

1. consider the image as an N x N matrix

2. choose an integer k∈ {0, 1, 2, 3}

3. rotate the square image k * 90 degree clockwise

4. if N is odd stop the encryption process

5. if N is even split the image into four equal sub-squares whose length is N / 2 and encrypt them recursively starting from step 0

Apparently different choices of the k serie result in different encrypted images. Given two images A and B, your task is to find out whether it is POSSIBLE that B is encrypted from A. B is possibly encrypted from A if there is a choice of k serie that encrypt A into B.

輸入
Input may contains multiple testcases.

The first line of the input contains an integer T(1 <= T <= 10) which is the number of testcases.

The first line of each testcase is an integer N, the length of the side of the images A and B.

The following N lines each contain N integers, indicating the image A.

The next following N lines each contain N integers, indicating the image B.

For 20% of the data, 1 <= n <= 15

For 100% of the data, 1 <= n <= 100, 0 <= Aij, Bij <= 100000000

輸出
For each testcase output Yes or No according to whether it is possible that B is encrypted from A.

樣例輸入
3
2
1 2
3 4
3 1
4 2
2
1 2
4 3
3 1
4 2
4
4 1 2 3
1 2 3 4
2 3 4 1
3 4 1 2
3 4 4 1
2 3 1 2
1 4 4 3
2 1 3 2
樣例輸出
Yes
No
Yes