A ski resort's cable-car network descends through m altitude tiers, each tier offering n stations side by side. Every station (i, j) — tier i, station j — has an integer congestion level g[i][j], where 0 <= g[i][j] <= L - 1 for some fixed number of possible congestion levels L. Riding the cable car away from a station whose congestion level is v, at some tier, down to station k of the very next tier, always charges a transfer toll of transferFee[v][k] — the toll depends only on the departing station's congestion level and the arriving station's index, never on which tier the move happens at.

A rider starts by choosing any single station on tier 1 and must ride down exactly one tier at a time until reaching tier m, ending at any station there. The total cost of a ride is the sum of the congestion levels of every station visited (one per tier, including the very first and the very last) plus the sum of every transfer toll paid along the way. The rider wants to choose a starting station and a full descent path that minimizes this total cost.

Determine that minimum possible total cost.

Input format

• Line 1: three space-separated integers m, n, L — the number of tiers, the number of stations per tier, and the number of distinct congestion levels.
• The next m lines each contain n space-separated integers: row i (0-indexed) gives g[i][0] ... g[i][n-1], the congestion levels of tier i's stations. Each value is between 0 and L-1 inclusive.
• The next L lines each contain n space-separated integers: row v (0-indexed) gives transferFee[v][0] ... transferFee[v][n-1], the toll for departing a station with congestion level v and arriving at station k of the next tier, for k = 0 ... n-1.

Output format

• A single integer: the minimum total cost of a descent from any tier-1 station to any tier-m station.

Constraints

• 2 <= m <= 50
• 1 <= n <= 50
• 1 <= L <= 50
• 0 <= g[i][j] <= L - 1
• 1 <= transferFee[v][k] <= 100

3 2 3
2 1
0 2
1 0
4 6
3 5
7 2

8

2 2 2
0 1
1 0
5 1
3 2

1