#include <bits/stdc++.h>
// #define int long long
#define endl '\n'
using namespace std;
const int N = 2e5+5;

struct node{
	double s,c;
	double sum;
	int lazy;
}t[N<<2];

int n,a[N];

inline void pushDown(int k,int mid,int l,int r){
	if(!t[k].lazy) return;

	t[k<<1].s = t[k<<1].s*cos(t[k].lazy*(mid-l+1)) + t[k<<1].c*sin(t[k].lazy*(mid-l+1));
	t[k<<1].c = t[k<<1].c*cos(t[k].lazy*(mid-l+1)) - t[k<<1].s*sin(t[k].lazy*(mid-l+1));
	t[k<<1].lazy += t[k].lazy;

	t[k<<1|1].s = t[k<<1|1].s*cos(t[k].lazy*(r-mid)) + t[k<<1|1].c*sin(t[k].lazy*(r-mid));
	t[k<<1|1].c = t[k<<1|1].c*cos(t[k].lazy*(r-mid)) - t[k<<1|1].s*sin(t[k].lazy*(r-mid));
	t[k<<1|1].lazy += t[k].lazy;

	t[k].lazy = 0;
}

inline void build(int k,int l,int r){
	if(l == r){
		t[k].s = sin(a[l]);
		t[k].c = cos(a[l]);
		return;
	}

	int mid = l + r >> 1;
	build(k<<1,l,mid);
	build(k<<1|1,mid+1,r);

	t[k].s = t[k<<1].s + t[k<<1|1].s;
	t[k].c = t[k<<1].c + t[k<<1|1].c;
}

inline void update(int k,int l,int r,int x,int y,int z){
	if(x <= l && r <= y){
		t[k].s = t[k].s*cos(z*(r-l+1)) + t[k].c*sin(z*(r-l+1));
		t[k].c = t[k].c*cos(z*(r-l+1)) - t[k].s*sin(z*(r-l+1));
		t[k].lazy += z;
		return;
	}

	int mid = l + r >> 1;
	pushDown(k,mid,l,r);
	if(x <= mid) update(k<<1,l,mid,x,y,z);
	if(y > mid) update(k<<1|1,mid+1,r,x,y,z);

	t[k].s = t[k<<1].s + t[k<<1|1].s;
	t[k].c = t[k<<1].c + t[k<<1|1].c;
}

inline double query(int k,int l,int r,int x,int y){
	if(x <= l && r <= y)
		return t[k].s;

	int mid = l + r >> 1;
	double res = 0;
	pushDown(k,mid,l,r);
	if(x <= mid) res += query(k<<1,l,mid,x,y);
	if(y > mid) res += query(k<<1|1,mid+1,r,x,y);

	return res;
}

signed main(){
	// ios::sync_with_stdio(0);
	// cin.tie(0);

    // freopen("app.in","r",stdin);
    // freopen("app.out","w",stdout);
	
	scanf("%d",&n);
	for(int i = 1; i <= n; i++)
		scanf("%d",&a[i]);

	build(1,1,n);

	int T,op,l,r,v;
	scanf("%d",&T);
	while(T--){
		scanf("%d%d%d",&op,&l,&r);
		if(op == 1){
			scanf("%d",&v);
			update(1,1,n,l,r,v);
		}else printf("%.1lf\n",query(1,1,n,l,r));
	}
	return 0;
}