human
Alice, the president of club FCB, wants to build a team for the new volleyball tournament. The team should consist of p players playing in p different positions. She also recognizes the importance of audience support, so she wants to select k people as part of the audience.

There are n people in Byteland. Alice needs to select exactly p players, one for each position, and exactly k members of the audience from this pool of n people. Her ultimate goal is to maximize the total strength of the club.

The i-th of the n persons has an integer a_{i} associated with him — the strength he adds to the club if he is selected as a member of the audience.

For each person i and for each position j, Alice knows s_{i, j} — the strength added by the i-th person to the club if he is selected to play in the j-th position.

Each person can be selected at most once as a player or a member of the audience. You have to choose exactly one player for each position.

Since Alice is busy, she needs you to help her find the maximum possible strength of the club that can be achieved by an optimal choice of players and the audience.

Input

The first line contains 3 integers n,p,k (2 ≤ n ≤ 10^{5}, 1 ≤ p ≤ 7, 1 ≤ k, p+k ≤ n).

The second line contains n integers a_{1},a_{2},…,a_{n}. (1 ≤ a_{i} ≤ 10^{9}).

The i-th of the next n lines contains p integers s_{i, 1}, s_{i, 2}, ..., s_{i, p}. (1 ≤ s_{i,j} ≤ 10^{9})

Output

Print a single integer {res} — the maximum possible strength of the club.

Examples

Input

4 1 2
1 16 10 3
18
19
13
15

Output

44

Input

6 2 3
78 93 9 17 13 78
80 97
30 52
26 17
56 68
60 36
84 55

Output

377

Input

3 2 1
500 498 564
100002 3
422332 2
232323 1

Output

422899

Note

In the first sample, we can select person 1 to play in the 1-st position and persons 2 and 3 as audience members. Then the total strength of the club will be equal to a_{2}+a_{3}+s_{1,1}.
impor
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Write me a Python code to find the maximum possible strength of the club that can be achieved by an optimal choice of players and the audience?
assistant
#Here is Python code to find the maximum possible strength of the club that can be achieved by an optimal choice of players and the audience.
t io
import os
from array import array

# Rewrote in C++

DEBUG = False

if DEBUG:
    from functools import lru_cache

    def solveTopDown(N, P, K, audienceScore, playerScore):
        # Choose P players and K audience members from N people
        assert len(audienceScore) == len(playerScore) == N

        # Sort both scores by audience score from largest to smallest
        scores = sorted(zip(audienceScore, playerScore), reverse=True)
        audienceScore = [a for a, p in scores]
        playerScore = [p for a, p in scores]

        @lru_cache(maxsize=None)
        def f(n, mask):
            # Return best score using up to the nth person with mask of positions used
            # Since we sorted by audience scores, we can take everyone not used in mask until exceed K
            if n == 0:
                # Single person
                if mask == 0:
                    # Not a player so must be an audience member
                    return audienceScore[n]
                else:
                    # Must be player at some position
                    for pos in range(P):
                        if mask == 1 << pos:
                            return playerScore[n][pos]
                    # Otherwise invalid
                    return float("-inf")

            # nth is neither audience nor player
            best = f(n - 1, mask)

            # Check if nth could be an audience member
            num = n + 1  # there are n + 1 people in 0 to n inclusive
            numPlayers = _popcount[mask]  # number of players in the mask
            if num - numPlayers <= K:
                # The audience members are always the first K not in mask and we are within that K
                best += audienceScore[n]

            # Try placing as a player, audience remains the same
            for pos in range(P):
                if (1 << pos) & mask:
                    best = max(best, playerScore[n][pos] + f(n - 1, mask - (1 << pos)))

            return best

        best = 0
        for i in range(N):
          ...