LUXURY 8

A - Gargari and Bishops

Time Limit:3000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u

Submit Status Practice CodeForces 463C

Description

Gargari is jealous that his friend Caisa won the game from the previous problem. He wants to prove that he is a genius.

He has a n × n chessboard. Each cell of the chessboard has a number written on it. Gargari wants to place two bishops on the chessboard in such a way that there is no cell that is attacked by both of them. Consider a cell with number x written on it, if this cell is attacked by one of the bishops Gargari will get x dollars for it. Tell Gargari, how to place bishops on the chessboard to get maximum amount of money.

We assume a cell is attacked by a bishop, if the cell is located on the same diagonal with the bishop (the cell, where the bishop is, also considered attacked by it).

Input

The first line contains a single integer n(2 ≤ n ≤ 2000). Each of the next n lines contains n integers a_ij(0 ≤ a_ij ≤ 10⁹) — description of the chessboard.

Output

On the first line print the maximal number of dollars Gargari will get. On the next line print four integers: x₁, y₁, x₂, y₂(1 ≤ x₁, y₁, x₂, y₂ ≤ n), where x_i is the number of the row where the i-th bishop should be placed, y_i is the number of the column where the i-th bishop should be placed. Consider rows are numbered from 1 to n from top to bottom, and columns are numbered from 1 to nfrom left to right.

If there are several optimal solutions, you can print any of them.

Sample Input

Input

4
1 1 1 1
2 1 1 0
1 1 1 0
1 0 0 1

Output

12
2 2 3 2

 做这道题会碰到2个问题：

1.如何很方便的得到每个“X”的值？经过yy可以发现矩阵上在"/"这种形状上i+j都为定值，而在""上i + n - j为定值，所以预处理出“" , "/"对应的数组，然后你就能在O(1)时间内得到每个”X"

2.如何能很快的知道两个“X"，符合题设的条件？多画几次你就会发现i+j为奇数，和偶数是，那两个叉肯定不会存在公共点。

观察很重要啊

 

 

 

B - Bits

Time Limit:1000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u

Submit Status Practice CodeForces 485C

Description

Let's denote as  the number of bits set ('1' bits) in the binary representation of the non-negative integer x.

You are given multiple queries consisting of pairs of integers l and r. For each query, find the x, such that l ≤ x ≤ r, and  is maximum possible. If there are multiple such numbers find the smallest of them.

Input

The first line contains integer n — the number of queries (1 ≤ n ≤ 10000).

Each of the following n lines contain two integers l_i, r_i — the arguments for the corresponding query (0 ≤ l_i ≤ r_i ≤ 10¹⁸).

Output

For each query print the answer in a separate line.

Sample Input

Input

3
1 2
2 4
1 10

Output

1
3
7

Hint

The binary representations of numbers from 1 to 10 are listed below:

1₁₀ = 1₂

2₁₀ = 10₂

3₁₀ = 11₂

4₁₀ = 100₂

5₁₀ = 101₂

6₁₀ = 110₂

7₁₀ = 111₂

8₁₀ = 1000₂

9₁₀ = 1001₂

10₁₀ = 1010₂

一个纯粹的贪心，可以按位一步一步贪。

C - No to Palindromes!

Time Limit:1000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u

Submit Status Practice CodeForces 465C

Description

Paul hates palindromes. He assumes that string s is tolerable if each its character is one of the first p letters of the English alphabet and sdoesn't contain any palindrome contiguous substring of length 2 or more.

Paul has found a tolerable string s of length n. Help him find the lexicographically next tolerable string of the same length or else state that such string does not exist.

Input

The first line contains two space-separated integers: n and p (1 ≤ n ≤ 1000; 1 ≤ p ≤ 26). The second line contains string s, consisting of n small English letters. It is guaranteed that the string is tolerable (according to the above definition).

Output

If the lexicographically next tolerable string of the same length exists, print it. Otherwise, print "NO" (without the quotes).

Sample Input

Input

3 3
cba

Output

NO

Input

3 4
cba

Output

cbd

Input

4 4
abcd

Output

abda

Hint

String s is lexicographically larger (or simply larger) than string t with the same length, if there is number i, such that s₁ = t₁, ..., s_i = t_i,s_i + 1 > t_i + 1.

The lexicographically next tolerable string is the lexicographically minimum tolerable string which is larger than the given one.

A palindrome is a string that reads the same forward or reversed.

一道构造题，构造题真是。。。。。

要做这道题，有个结论非常重要，那就是只有“部分对称” ， 才会有可能性造成“整体堆成”，所以只要破坏所有“部分对称“，就行了。

而部分对称只有两种形式”aa” ， “aba”

 

 

D - George and Job

Time Limit:1000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u

Submit Status Practice CodeForces 467C

Description

The new ITone 6 has been released recently and George got really keen to buy it. Unfortunately, he didn't have enough money, so George was going to work as a programmer. Now he faced the following problem at the work.

Given a sequence of n integers p₁, p₂, ..., p_n. You are to choose k pairs of integers:

[l₁, r₁], [l₂, r₂], ..., [l_k, r_k] (1 ≤ l₁ ≤ r₁ < l₂ ≤ r₂ < ... < l_k ≤ r_k ≤ n; r_i - l_i + 1 = m), 

in such a way that the value of sum  is maximal possible. Help George to cope with the task.

Input

The first line contains three integers n, m and k(1 ≤ (m × k) ≤ n ≤ 5000). The second line contains n integers p₁, p₂, ..., p_n(0 ≤ p_i ≤ 10⁹).

Output

Print an integer in a single line — the maximum possible value of sum.

Sample Input

Input

5 2 1
1 2 3 4 5

Output

9

Input

7 1 3
2 10 7 18 5 33 0

Output

61

 一道裸的dp，一开始需要转移的状态没有想清楚，然后学长提醒后，很快就想到了，我用dp[前i个人][j个组] = max (当前i为第j组的最后一人 ，dp[i-1][j])

转移的状态真心要想清楚啊。