c.cpp

#include<iostream>
#include<sstream>
#include<string>
#include<cmath>
#include<cstdio>
#include<vector>
#include<map>
#include<set>
#include<queue>
#include<deque>
#include<algorithm>
#include<functional>
#include<numeric>
#define rep(i,b)
using namespace std;

int main(){

	while(1){
		int n,r;
		cin >> r >> n;
		if(n==0&&r==0)break;

		bool block[20][20];
		for(int i=0;i<20;i++){
			for(int j=0;j<20;j++){
				block[i][j]=false;

			}
		}

		for(int i=0;i<n;i++){
			int xl,xr,h;
			cin >>xl>>xr>>h;
			for(int j=xl;j<xr;j++){
				for(int k=0;k<h;k++){block[j][k]=true;}
			}
		}

		int f=0;
		for(int i=-r;i<r;i++){

			if(block[i][0]==false){f=1;cout << "0.0000" <<endl;}
		}
		if(f==1){continue;}

		vector < pair<int,int> > kado;
/*
		for(int i=-1;i<1;i++){
			for(int j=20;j>0;j--){
				if(block[i][j]==true){
					kado.push_back((pair<int,int>(0,j+1)));
				}
			}
		}*/

		for(int i=0;i<r;i++){
			for(int j=20;j>0;j--){
				if(block[i][j]==true){
					kado.push_back( (pair<int,int>(i,j+1)));
				}
			}
		}

		for(int i=-1;i>-r;i--){
			for(int j=20;j>0;j--){
				if(block[i][j]==true){
					kado.push_back( pair<int,int>(i,j+1));
				}
			}
		}

		float result = 20+r;

		for(int i=0;i<kado.size();i++){
			float y = r*r-((kado[i].first)*(kado[i].first));
			y = sqrt(y);
			//printf("%f",kado[i].second-y+r );cout <<endl; 
			result=min(result,kado[i].second-y+r);
		}

		printf("%.4f",result);
		cout << endl;




	}
}