Problem:
Score : 900 points

Problem Statement

In the city of Nevermore, there are 10^8 streets and 10^8 avenues, both numbered from 0 to 10^8-1.
All streets run straight from west to east, and all avenues run straight from south to north.
The distance between neighboring streets and between neighboring avenues is exactly 100 meters.

Every street intersects every avenue. Every intersection can be described by pair (x, y), where x is avenue ID and y is street ID.

There are N fountains in the city, situated at intersections (X_i, Y_i).
Unlike normal intersections, there's a circle with radius 10 meters centered at the intersection, and there are no road parts inside this circle.

The picture below shows an example of how a part of the city with roads and fountains may look like.

City governors don't like encountering more than one fountain while moving along the same road.
Therefore, every street contains at most one fountain on it, as well as every avenue.

Citizens can move along streets, avenues and fountain perimeters.
What is the shortest distance one needs to cover in order to get from intersection (x_1, y_1) to intersection (x_2, y_2)?

Constraints

0 \leq x_1, y_1, x_2, y_2 < 10^8

1 \leq N \leq 200,000

0 \leq X_i, Y_i < 10^8

X_i \neq X_j for i \neq j

Y_i \neq Y_j for i \neq j

Intersections (x_1, y_1) and (x_2, y_2) are different and don't contain fountains.

All input values are integers.

Input

Input is given from Standard Input in the following format:

x_1 y_1 x_2 y_2
N
X_1 Y_1
X_2 Y_2
:
X_N Y_N

Output

Print the shortest possible distance one needs to cover in order to get from intersection (x_1, y_1) to intersection (x_2, y_2), in meters.
Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-11}.

Sample Input 1

1 1 6 5
3
3 2
5 3
2 4

Sample Output 1

891.415926535897938

One possible shortest path is shown on the picture below. The path starts at the blue point, finishes at the purple point and follows along the red line.

Sample Input 2

3 5 6 4
3
3 2
5 3
2 4

Sample Output 2

400.000000000000000

Sample Input 3

4 2 2 2
3
3 2
5 3
2 4

Sample Output 3

211.415926535897938

Solution in C (GCC 5.4.1) (judge verdict: Wrong Answer)

/*
cat <<EOF >mistaken-paste
*/

#pragma GCC diagnostic ignored "-Wincompatible-pointer-types"
#define _USE_MATH_DEFINES

#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>
#include <time.h>

#define BIG 2000000007
#define VERYBIG 200000000000007LL

#define MOD 1000000007
#define FOD  998244353
typedef uint64_t ull;
typedef  int64_t sll;

#define N_MAX 300000
#define M_MAX 200000

#ifdef __cplusplus
#include <queue>
#include <stack>
// #include <tuple>
#include <set>
#include <map>

// using namespace std; // HELL
using std::queue;
using std::priority_queue;
using std::stack;
// using std::tuple;
using std::set;
using std::map;
using std::vector;
using std::greater;
using std::pair;

#endif

typedef struct {
	int32_t a;
	int32_t b;
} hw;

typedef struct {
	sll a;
	sll b;
} hwll;

typedef struct {
	sll a;
	sll b;
	sll c;
} hwllc;

typedef struct {
	hwll a;
	hwll b;
} linell;

ull n, m;
ull h, w;
ull k;
ull q;
ull vua, vub, vuc, vud, vue, vuf;
sll vsa, vsb, vsc, vsd, vse, vsf;
long double vra, vrb, vrc;
double vda, vdb, vdc;
size_t slen;
size_t tlen;
char ch, dh;

ull umin (ull x, ull y) {
	return (x < y) ? x : y;
}

ull umax (ull x, ull y) {
	return (x > y) ? x : y;
}

sll smin (sll x, sll y) {
	return (x < y) ? x : y;
}

sll smax (sll x, sll y) {
	return (x > y) ? x : y;
}

ull gcd (ull x, ull y) {
	if (x < y) {
		return gcd(y, x);
	} else if (y == 0) {
		return x;
	} else {
		return gcd(y, x % y);
	}
}

ull bitpow (ull a, ull x, ull modulo) {
	ull result = 1;
	while (x) {
		if (x & 1) {
			result *= a;
			result %= modulo;
		}
		x /= 2;
		a = (a * a) % modulo;
	}
	return result;
}

ull divide (ull a, ull b, ull modulo) {
	return (a * bitpow(b, modulo - 2, modulo)) % modulo;
}

ull udiff (ull a, ull b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

sll sdiff (sll a, sll b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

void printUquotient (ull left, ull right) {
	const int32_t digits = 20;

	printf("%llu.", left / right);
	left %= right;
	for (int32_t i = 0; i < digits; i++) {
		left *= 10;
		printf("%1d", left / right);
		left %= right;
	}
	puts("");

	return;
}

void printSquotient (sll left, sll right) {
	if (left * right < 0) putchar('-');
	printUquotient(sdiff(left, 0), sdiff(right, 0));

	return;
}

int bitcount (ull n) {
	int result = 0;
	while (n) {
		if (n & 1) result++;
		n /= 2;
	}
	return result;
}

#ifdef __cplusplus

bool setfind (set<ull> s, ull x) {
	return (s.find(x) != s.end());
}

#endif

// double distance (sll x1, sll y1, sll x2, sll y2) {
// 	double xdist2, ydist2, origindist, dist;

// 	xdist2 = (x1 - x2) * (x1 - x2);
// 	ydist2 = (y1 - y2) * (y1 - y2);
// 	return sqrt(xdist2 + ydist2);
// }

int32_t pullcomp (const void *left, const void *right) {
	ull l = *(ull*)left;
	ull r = *(ull*)right;
	if (l < r) {
		return -1;
	}
	if (l > r) {
		return +1;
	}
	return 0;
}

int32_t psllcomp (const void *left, const void *right) {
	sll l = *(sll*)left;
	sll r = *(sll*)right;
	if (l < r) {
		return -1;
	}
	if (l > r) {
		return +1;
	}
	return 0;
}

int32_t pcharcomp (const void *left, const void *right) {
	char l = *(char*)left;
	char r = *(char*)right;
	if (l < r) {
		return -1;
	}
	if (l > r) {
		return +1;
	}
	return 0;
}

int32_t pstrcomp (const void *left, const void *right) {
	char* l = *(char**)left;
	char* r = *(char**)right;

	return strcmp(l, r);
}

int32_t phwllABcomp (const void *left, const void *right) {
	hwll l = *(hwll*)left;
	hwll r = *(hwll*)right;
	if (l.a < r.a) {
		return -1;
	}
	if (l.a > r.a) {
		return +1;
	}
	if (l.b < r.b) {
		return -1;
	}
	if (l.b > r.b) {
		return +1;
	}
	return 0;
}

int32_t ptriplecomp (const void *left, const void *right) {
	hwllc l = *(hwllc*)left;
	hwllc r = *(hwllc*)right;

	if (l.a < r.a) {
		return -1;
	}
	if (l.a > r.a) {
		return +1;
	}
	if (l.b < r.b) {
		return -1;
	}
	if (l.b > r.b) {
		return +1;
	}
	if (l.c < r.c) {
		return -1;
	}
	if (l.c > r.c) {
		return +1;
	}
	return 0;
}

bool isinrange (sll left, sll x, sll right) {
	return (left <= x && x <= right);
}

bool isinrange_soft (sll left, sll x, sll right) {
	return (left <= x && x <= right) || (left >= x && x >= right);
}

ull parent[N_MAX];
ull rank[N_MAX];
void uf_init (ull n) {
	for (sll i = 0; i < n; i++) {
		parent[i] = i;
		rank[i] = 0;
	}
}
ull uf_find (ull x) {
	if (parent[x] == x) return x;
	return parent[x] = uf_find(parent[x]);
}
bool uf_union (ull a, ull b) {
	a = uf_find(a);
	b = uf_find(b);
	if (a == b) return false;

	if (rank[a] > rank[b]) {
		parent[b] = a;
	} else {
		parent[a] = b;
		if (rank[a] == rank[b]) {
			rank[b]++;
		}
	}
	return true;
}


sll a[N_MAX];
// sll a[3001][3001];
sll b[N_MAX];
sll c[N_MAX];
// char s[N_MAX + 1];
char s[3010][3010];
char t[N_MAX + 1];
hwll xy[N_MAX];

ull lis[N_MAX + 1];

ull solve () {
	sll i, j, ki, li;
	// ull result = 0;
	sll result = 0;
	double dresult = 0;
	// ull maybe = 0;
	sll maybe = 0;
	// ull sum = 0;
	sll sum = 0;
	sll item;
	ull *dpcell;

	if (vua > vuc) {
		const ull maxv = 100000000;
		for (i = 0; i < n; i++) {
			xy[i].a = maxv - xy[i].a;
		}
		vua = maxv - vua;
		vuc = maxv - vuc;
	}
	if (vub > vud) {
		const ull maxv = 100000000;
		for (i = 0; i < n; i++) {
			xy[i].b = maxv - xy[i].b;
		}
		vub = maxv - vub;
		vud = maxv - vud;
	}

	ull len = 0;
	qsort(xy, n, sizeof(hwll), phwllABcomp);
	for (i = 0; i < n; i++) {
		if (isinrange_soft(vua, xy[i].a, vuc) && isinrange_soft(vub, xy[i].b, vud)) {
			// hwll x = {xy[i].b, len};
			// printf("%lld,%lld!\n", xy[i].b, len);
			// sorted[len++] = x;
			a[len++] = xy[i].b;

		}
	}
	// qsort(sorted, len, sizeof(hwll), phwllABcomp);

	for (i = 0; i <= len; i++) {
		lis[i] = (i ? BIG : 0);
	}
	ull lislen = 0;

	for (i = 0; i < len; i++) {
		// item = sorted[i].b;
		item = a[i];

		sll ok = 0, ng = lislen + 1;
		while (ok + 1 < ng) {
			ull med = (ok + ng) / 2;
			if (lis[med] < item) {
				ok = med;
			} else {
				ng = med;
			}
		}

		if (item < lis[ng]) {
			lis[ng] = item;
			lislen = umax(lislen, ng);
		}
	}

	const double quarter = M_PI * 5;

	dresult = (udiff(vua, vuc) + udiff(vub, vud)) * 100LL;
	if (vua == vuc || vub == vud) {
		dresult += (quarter * 2 - 20) * (double)lislen;
	} else {
		dresult -= (20 - quarter) * (double)lislen;
	}

	// printf("%lld\n", result);
	printf("%.15lf\n", dresult);
	// puts(s);

	return 0;

	success:
	puts("YES");
	// puts("Yes");
	// printf("%llu\n", result);
	// puts("0");
	// puts("Takahashi");
	return 0;

	fail:
	puts("NO");
	// puts("No");
	// puts("0");
	// puts("-1");
	// puts("-1 -1 -1");
	// puts("Aoki");
	return 1;
}

int32_t main (void) {
	int32_t i, j;
	int32_t x, y;

	// scanf("%lf%lf", &vda, &vdb, &vdc);
	// scanf("%lld%lld", &vsa, &vsb, &vsc, &vsd);
	scanf("%llu%llu%llu%llu", &vua, &vub, &vuc, &vud);
	// scanf("%*llu%*llu");
	// scanf("%llu%llu", &h, &w);
	scanf("%llu", &n, &m);
	// scanf("%llu", &k, &n);
	// scanf("%llu%llu%llu%llu", &vua, &vub, &vuc, &vud, &vue, &vuf);
	// vua--;
	// vub--;
	// vuc--;
	// vud--;
	// scanf("%lld%lld", &vsa, &vsb, &vsc);
	// scanf("%s", s);
	// scanf("%s", t);
	// scanf("%llu", &k);
	// scanf("%llu", &q);
	for (i = 0; i < n; i++) {
		// scanf("%lld", &a[i]);
		// scanf("%lld", &b[i]);
		scanf("%lld%lld", &xy[i].a, &xy[i].b);
		// scanf("%llu", &c[i]);
		// a[i]--;
		// b[i]--;
		// c[i]--;
	}
	// for (i = 0; i < m; i++) {
	// 	scanf("%llu", &b[i]);
	// }
	// scanf("%llu", &q);

	// for (i = 0; i < n; i++) {
	// 	for (j = 0; j < n; j++) {
	// 		scanf("%llu", &a[i][j]);
	// 	}
	// }
	// for (i = 0; i < h; i++) {
	// 	scanf("%s", &s[i]);
	// }

	// scanf("%llu", &k);
	// scanf("%llu", &q);

	solve();

	return 0;
}