abc259 d

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

using ll = long long;
using pii = pair<ll, ll>;
using p3i = pair<pii, ll>;

int n, sx, sy, tx, ty;
vector<p3i> cs;

vector<int> fa;
void init(int n) { fa = vector<int>(n, -1); }
int find(int x)
{
    if (fa[x] == -1)
        return x;
    return fa[x] = find(fa[x]);
}
int join(int x, int y)
{
    int px = find(x);
    int py = find(y);
    if (px == py) {
        return px;
    }
    return fa[py] = px;
}

long double epsilon = 1e-7;
long double dist(ll x1, ll y1, ll x2, ll y2)
{
    long double dx = (long double) (x1) -x2;
    long double dy = (long double) (y1) -y2;
    return sqrt(dx * dx + dy * dy);
}

ll dist_sq(ll x1, ll y1, ll x2, ll y2)
{
    ll dx = x1 - x2;
    ll dy = y1 - y2;
    return dx * dx + dy * dy;
}
bool pts_on_cirle(ll x, ll y, const p3i &c)
{
    // return abs(dist(x, y, c.first.first, c.first.second) - c.second) <= epsilon;
    return dist_sq(x, y, c.first.first, c.first.second) == c.second * c.second;
}

bool circles_sect(const p3i &c1, const p3i &c2)
{
    ll x1 = c1.first.first, y1 = c1.first.second, x2 = c2.first.first, y2 = c2.first.second;
    /*
    long double r1 = c1.second, r2 = c2.second;
    if (dist(x1, y1, x2, y2) > r1 + r2 + epsilon) {
        return false;
    }
    if (dist(x1, y1, x2, y2) + epsilon < abs(r1 - r2)) {
        return false;
    }
    return true;
    */
    ll r1 = c1.second, r2 = c2.second;
    if (dist_sq(x1, y1, x2, y2) > (r1 + r2) * (r1 + r2)) {
        return false;
    }
    if (dist_sq(x1, y1, x2, y2) < (r1 - r2) * (r1 - r2)) {
        return false;
    }
    return true;
}

int main(int argc, char **argv)
{
    scanf("%d", &n);
    cs = vector<p3i>(n + 1);
    scanf("%d%d%d%d", &sx, &sy, &tx, &ty);
    ll x, y, r;

    for (int i = 0; i < n; ++i) {
        scanf("%lld%lld%lld", &x, &y, &r);
        cs[i] = {{x, y}, r};
    }
    init(n);
    int fs = -1, ft = -1;
    for (int i = 0; i < n; ++i) {
        if (pts_on_cirle(sx, sy, cs[i]))
            fs = i;
        if (pts_on_cirle(tx, ty, cs[i]))
            ft = i;
        for (int j = i + 1; j < n; ++j) {
            if (circles_sect(cs[i], cs[j])) {
                join(i, j);
            }
        }
    }
    if (fs == -1 || ft == -1) {
        printf("No\n");
    } else {
        printf("%s\n", (find(fs) == find(ft) ? "Yes" : "No"));
    }

    return 0;
};