Problem: Hit n nails one by one at the coordinates P1 (x1, y1), P2 (x2, y2), P3 (x3, y3), ..., Pn (xn, yn) on the flat plate, and put them on the rubber band ring. Surround it with a single rubber band so that all the nails fit inside. At this time, the rubber bands must not intersect.

Create a program that reads the coordinates of the nails and outputs the number of nails that are not in contact with the rubber band when the nail is surrounded by the rubber band as described above. The rubber band shall expand and contract sufficiently. You may not hit more than one nail at the same coordinates. In addition, it is assumed that the nails covered with rubber bands are connected by a straight line, and that no more than three nails are lined up on the straight line. For example, there can be no input as shown in Figure 1. As shown in Figure 2, it is possible for nails without rubber bands to line up in a straight line.

<image> | <image>
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Figure 1 | Figure 2



However, each coordinate value is a real number between -1000.0 and 1000.0. Also, n is an integer between 3 and 100.

Hint

Below is a diagram for the second sample input.

<image>
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Input

Given multiple datasets. Each dataset is given in the following format:


n
x1, y1
x2, y2
...
...
xn, yn


When n is 0, it indicates the end of input. The number of datasets does not exceed 50.

Output

For each dataset, output the number of nails that are not in contact with the rubber. For example, if there is an input representing the four nails shown in Fig. 3, it will be surrounded as shown in Fig. 4, so the number of nails that are not in contact with the rubber band is one.

<image> | <image>
--- | ---
Figure 3 | Figure 4


Example

Input

4
1.0,0.0
0.0,1.0
2.0,1.0
1.0,2.0
9
-509.94,892.63
567.62,639.99
-859.32,-64.84
-445.99,383.69
667.54,430.49
551.12,828.21
-940.2,-877.2
-361.62,-970
-125.42,-178.48
0


Output

0
3

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

using uint=unsigned;
using ll=long long;
using ull=unsigned long long;
#define int ll

#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=a;i--)
#define per(i,b) gnr(i,0,b)
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define eb emplace_back
#define fs first
#define sc second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif
#define tmp template<class t>

tmp void chmax(t&a,t b){if(a<b)a=b;}
tmp void chmin(t&a,t b){if(a>b)a=b;}

tmp using vc=vector<t>;
tmp using vvc=vc<vc<t>>;

using pi=pair<int,int>;
using vi=vc<int>;

template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
	return os<<"{"<<p.fs<<","<<p.sc<<"}";
}

tmp ostream& operator<<(ostream& os,const vc<t>& v){
	os<<"{";
	for(auto e:v)os<<e<<",";
	return os<<"}";
}

constexpr ll ten(int n){
	return n==0?1:ten(n-1)*10;
}

tmp void mkuni(vc<t>&v){
	sort(all(v));
	v.erase(unique(all(v)),v.ed);
}

ll read(){ll i;cin>>i;return i;}

using ld=long double;
using cm=complex<ld>;
#define x real()
#define y imag()
const ld eps=1e-7;
int sgn(ld a){return a<-eps?-1:(a>eps?1:0);}
auto cmcmp=[](const cm&a,const cm&b){
	if(sgn(a.x-b.x))return a.x<b.x;
	else return sgn(a.y-b.y)<0;
};

ld dot(cm a,cm b){return a.x*b.x+a.y*b.y;}
ld crs(cm a,cm b){return a.x*b.y-a.y*b.x;}
int ccw(cm a,cm b){return sgn(crs(a,b));}
int ccw(cm a,cm b,cm c){return ccw(b-a,c-a);}

//(-2)[a,-1](0)[b,1](2)
int bet(cm a,cm b,cm c){
	cm d=b-a;
	ld e=dot(d,c-a);
	if(sgn(e)<=0)return sgn(e)-1;
	return sgn(e-norm(d))+1;
}

ld tri2(cm a,cm b,cm c){
	return crs(b-a,c-a);
}

//0-no,1-edge,2-in
int cont(cm a,cm b,cm c,cm d){
	if(ccw(a,b,c)==-1)
		swap(b,c);
	return min({ccw(a,b,d),ccw(b,c,d),ccw(c,a,d)})+1;
}

//no point in edges
vc<cm> convex(vc<cm> s){
	swap(s[0],*min_element(all(s),cmcmp));
	sort(s.bg+1,s.ed,[&](cm a,cm b){
		int c=ccw(s[0],a,b);
		if(c)return c==1;
		else return bet(s[0],a,b)==2;
	});
	vc<cm> t;
	rep(i,s.size()){
		int ss;
		while((ss=t.size())>=2){
			cm a=t[ss-2];
			cm b=t[ss-1];
			cm c=s[i];
			if(ccw(a,b,c)>0)
				break;
			t.pop_back();
		}
		t.pb(s[i]);
	}
	return t;
}

cm readcm(){
	ld a,b;
	char c;
	cin>>a>>c>>b;
	return cm(a,b);
}

ld readld(){
	ld a;
	cin>>a;
	return a;
}

signed main(){
	cin.tie(nullptr);
	ios::sync_with_stdio(false);
	cout<<fixed<<setprecision(20);
	while(1){
		int n=read();
		if(n==0)break;
		vc<cm> s(n);
		rep(i,n)
			s[i]=readcm();
		cout<<n-convex(s).size()<<endl;
	}
}