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| #include <iostream>
#include <vector>
#include <string>
#include <cstring>
#include <algorithm>
#include <sstream>
#include <map>
#include <set>
#include <cmath>
#define REP(i,k,n) for(int i=k;i<n;i++)
#define rep(i,n) for(int i=0;i<n;i++)
#define INF 1<<30
#define pb push_back
#define mp make_pair
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
int main() {
int r, n;
while(cin >> r >> n) {
if(r == 0 && n == 0) break;
vector<pair<int, P> > v(n);
rep(i, n) cin >> v[i].second.first >> v[i].second.second >> v[i].first;
int H[60], GETA = 30;
memset(H, 0, sizeof(H));
rep(i, n) {
int h = v[i].first, x1 = v[i].second.first, x2 = v[i].second.second;
REP(j, x1, x2) {
H[j + GETA] = max(H[j + GETA], h);
}
}
double ans = INF;
REP(i, -r+1, r) {
double res = r + min(H[i + GETA], H[i - 1 + GETA]);
ans = min(ans, res - sqrt(r*r - i*i));
}
cout << fixed;
cout.precision(4);
cout << ans << endl;
}
return 0;
}
|
