#include "wombats.h"
#include <string.h>
#define N 5000
#define M 200
#define M_ 10
#define N_ (1 << 9)
#define INF 0x3f3f3f3f
int min(int a, int b) { return a < b ? a : b; }
int max(int a, int b) { return a > b ? a : b; }
int aa[N][M - 1], bb[N - 1][M], n, m, st[N_ * 2][M][M];
void pul(int i) { /* http://blog.brucemerry.org.za/2013/07/ioi-2013-day-1-analysis.html (Knuth's optimization) */
static int jj2[M][M];
int l = i << 1, r = l | 1, d, j1, j2, j3;
for (j1 = 0; j1 < m; j1++)
memset(st[i][j1], 0x3f, m * sizeof *st[i][j1]);
for (d = m - 1; d >= -(m - 1); d--)
for (j1 = max(-d, 0); j1 < m && (j3 = j1 + d) < m; j1++) {
int jl = j1 == 0 ? 0 : jj2[j1 - 1][j3], jr = j3 + 1 == m ? m - 1 : jj2[j1][j3 + 1], j2_, d_;
j2_ = -1, d_ = INF * 2 + 1;
for (j2 = jl; j2 <= jr; j2++) {
int d = st[l][j1][j2] + st[r][j2][j3];
if (d_ > d)
d_ = d, j2_ = j2;
}
st[i][j1][j3] = min(d_, INF), jj2[j1][j3] = j2_;
}
}
void solve(int i_) {
int l = i_ * M_, r = min((i_ + 1) * M_, n - 1), i, j, js;
for (js = 0; js < m; js++) {
int *dp = st[N_ + i_][js], x;
if (l >= r)
memset(dp, 0x3f, m * sizeof *dp), dp[js] = 0;
else {
dp[js] = 0;
for (j = js + 1; j < m; j++)
dp[j] = dp[j - 1] + aa[l][j - 1];
for (j = js - 1; j >= 0; j--)
dp[j] = dp[j + 1] + aa[l][j];
for (i = l + 1; i <= r; i++) {
for (j = 0; j < m; j++) {
dp[j] += bb[i - 1][j];
if ((i < r || i == n - 1) && j > 0 && dp[j] > (x = dp[j - 1] + aa[i][j - 1]))
dp[j] = x;
}
if (i < r || i == n - 1)
for (j = m - 2; j >= 0; j--)
if (dp[j] > (x = dp[j + 1] + aa[i][j]))
dp[j] = x;
}
}
}
}
void init(int n_, int m_, int A[5000][200], int B[5000][200]) {
int i;
n = n_, m = m_;
for (i = 0; i < n; i++)
memcpy(aa[i], A[i], (m - 1) * sizeof *A[i]);
for (i = 0; i < n - 1; i++)
memcpy(bb[i], B[i], m * sizeof *B[i]);
for (i = 0; i < N_; i++)
solve(i);
for (i = N_ - 1; i > 0; i--)
pul(i);
}
void update(int i) {
solve(i), i += N_;
while (i > 1)
pul(i >>= 1);
}
void changeH(int i, int j, int w) {
aa[i][j] = w;
update(i % M_ == 0 && i == n - 1 ? i / M_ - 1 : i / M_);
}
void changeV(int i, int j, int w) {
bb[i][j] = w;
update(i / M_);
}
int escape(int js, int jt) {
return st[1][js][jt];
}
