// Problem: F - Tile Distance
// Contest: AtCoder - AtCoder Beginner Contest 353
// URL: https://atcoder.jp/contests/abc353/tasks/abc353_f
// Memory Limit: 1024 MB
// Time Limit: 2000 ms
//
// Powered by CP Editor (https://cpeditor.org)
#include <bits/stdc++.h>
using namespace std;
#define ll long long
bool large(ll bx, ll by) {
return (bx + by) & 1;
}
// X-1,X+1,Y-1,Y+1
ll s_to_l(ll x, ll y, ll sz, int dir) {
x %= sz, y %= sz;
if (dir == 0) {
return x + 1;
} else if (dir == 1) {
return sz - x;
} else if (dir == 2) {
return y + 1;
} else {
return sz - y;
}
}
ll dis_l(ll bx1, ll by1, ll bx2, ll by2, ll sz) {
if (sz == 1) {
return abs(bx1 - bx2) + abs(by1 - by2);
} else if (sz == 2) {
ll ans = min(abs(bx1 - bx2), abs(by1 - by2)) * 2;
ans += (max(abs(bx1 - bx2), abs(by1 - by2)) - min(abs(bx1 - bx2), abs(by1 - by2))) / 2 * 3;
return ans;
}
return max(abs(bx1 - bx2), abs(by1 - by2)) * 2;
}
ll dx[] = {-1, 1, 0, 0};
ll dy[] = {0, 0, -1, 1};
int main() {
ll sz;
scanf("%lld", &sz);
ll sx, sy, tx, ty;
scanf("%lld %lld", &sx, &sy);
scanf("%lld %lld", &tx, &ty);
ll bsx = sx / sz, bsy = sy / sz, btx = tx / sz, bty = ty / sz;
// Case 1: L vs L
// Case 2: L vs S
// Case 3: S vs S
// Case 4: same L
// Case 5: same S
if (bsx == btx && bsy == bty) {
// Case 4/5
if (large(bsx, bsy)) {
// Case 4
cerr << 4;
puts("0");
} else {
// Case 5
cerr << 5;
printf("%lld", abs(sx - tx) + abs(sy - ty));
}
} else {
// Case 1/2/3
if (large(bsx, bsy) && large(btx, bty)) {
// Case 1
cerr << 1;
printf("%lld", dis_l(bsx, bsy, btx, bty, sz));
} else if (!large(bsx, bsy) && !large(btx, bty)) {
// Case 3
cerr << 3;
ll ans = 0x3f3f3f3f3f3f3f3fll;
for (int i = 0; i < 4; i++) {
for (int j = 0; j < 4; j++) {
ans = min(ans, s_to_l(sx, sy, sz, i) + s_to_l(sx, sy, sz, j) + dis_l(bsx + dx[i], bsy + dy[i], btx + dx[j], bty + dy[j], sz));
}
}
printf("%lld", ans);
} else {
// Case 2
cerr << 2;
if (!large(bsx, bsy)) {
swap(bsx, btx);
swap(bsy, bty);
swap(sx, tx);
swap(sy, ty);
}
ll ans = 0x3f3f3f3f3f3f3f3fll;
for (int i = 0; i < 4; i++) {
ans = min(ans, s_to_l(tx, ty, sz, i) + dis_l(bsx, bsy, btx + dx[i], bty + dy[i], sz));
}
printf("%lld", ans);
}
}
}
大致思路就是分成五类,第一类从L到L,第二类从L到S,第三类从S到S,第四类同在一个L内,第五类不需要经过L