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Cod sursa(job #863122)
#include <cstdio>
#include <iostream>
#include <fstream>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <bitset>
#include <algorithm>
#include <sstream>
#include <iomanip>
#include <cmath>
#include <cstdlib>
#include <ctype.h>
#include <cstring>
#include <ctime>
#include <cassert>
#include <utility>
using namespace std;
#define INF 1e15
#define MAXN 255
struct Point {
int x, y;
};
int N;
Point P[MAXN];
int FIRST;
int st[MAXN];
int head;
char distr1[MAXN], distr2[MAXN];
string minDistr;
long long crossProduct(const Point &A, const Point &B, const Point &C) {
return (long long)(B.x - A.x) * (C.y - A.y) - (long long)(B.y - A.y) * (C.x - A.x);
}
bool cmp(const int &A, const int &B) {
return crossProduct(P[FIRST], P[A], P[B]) > 0;
}
void convexHull(vector<int> &pts, vector<int> &R) {
size_t first = 0;
for(size_t i = 0; i < pts.size(); i++)
if(P[pts[i]].y < P[pts[first]].y)
first = i;
swap(pts[first], pts[0]);
FIRST = pts[0];
sort(pts.begin(), pts.end(), cmp);
st[0] = pts[0];
st[1] = pts[1];
head = 1;
for(size_t i = 2; i < pts.size(); i++) {
while(head >= 1 && crossProduct(P[st[head - 1]], P[st[head]], P[pts[i]]) < 0) // > 1 ?
head--;
st[++head] = pts[i];
}
for(int i = 0; i <= head; i++)
R.push_back(st[i]);
}
double ariePoligon(vector<int> &pts) {
double ret = 0.0;
for(size_t i = 1; i + 1 < pts.size(); i++)
ret += crossProduct(P[pts[0]], P[pts[i]], P[pts[i + 1]]);
return fabs(ret / 2.0);
}
string getDistr(vector<int> P[2]) {
for(int i = 0; i < 2; i++)
for(size_t j = 0; j < P[i].size(); j++) {
if(i == 0) {
distr1[P[i][j]] = 'I';
distr2[P[i][j]] = 'V';
}
else {
distr1[P[i][j]] = 'V';
distr2[P[i][j]] = 'I';
}
}
string v1(distr1);
string v2(distr2);
return min(v1, v2);
}
int main() {
freopen("gradina.in", "r", stdin);
freopen("gradina.out","w", stdout);
scanf("%d", &N);
for(int i = 0; i < N; i++)
scanf("%d %d", &P[i].x, &P[i].y);
double minDiff = INF;
for(int x = 0; x < N; x++)
for(int y = 0; y < N; y++)
if(x != y) {
vector<int> sp[2];
sp[0].push_back(x);
sp[1].push_back(y);
for(int i = 0; i < N; i++)
if(i != x && i != y) {
long long cp = crossProduct(P[x], P[y], P[i]);
int side = (cp > 0);
sp[side].push_back(i);
}
vector<int> inf[2];
convexHull(sp[0], inf[0]);
if(sp[0].size() != inf[0].size())
continue;
convexHull(sp[1], inf[1]);
if(sp[1].size() != inf[1].size())
continue;
double arie[2];
arie[0] = ariePoligon(inf[0]);
arie[1] = ariePoligon(inf[1]);
double diff = fabs(arie[0] - arie[1]);
if(diff < minDiff) {
minDiff = diff;
minDistr = getDistr(inf);
}
else if(diff == minDiff) {
string s = getDistr(inf);
if(s < minDistr)
minDistr = s;
}
}
printf("%.6lf\n", minDiff);
printf("%s\n", minDistr.c_str());
return 0;
}