#include <stdio.h>
#include <sstream>
#include <iostream>
#include <fstream>
#include <string.h>
#include <vector>
#include <map>
#include <algorithm>
#include <utility>
#include <set>
#include <cctype>
#include <queue>
#include <stack>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <deque>
#include <limits>
#include <iomanip>
#include <ctype.h>
#include <unordered_map>
#include <random>
#include <bitset>

#define _USE_MATH_DEFINES
#include <iostream>
#include <math.h>
#include <complex>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<ll, double> pld;
typedef pair<double, double> pdd;
typedef pair<double, ll> pdl;
typedef pair<int, char> pic;
typedef vector<ll> vl;
typedef vector<int> vi;
typedef priority_queue<ll, vector<ll>, greater<ll>> llgreaterq;
typedef priority_queue<pll, vector<pll>, greater<pll>> pllgreaterq;
typedef priority_queue<pair<ll, pll>, vector<pair<ll, pll>>, greater<pair<ll, pll>>> plpllgreaterq;
typedef priority_queue<vi, vector<vi>, greater<vi>> vigreaterq;
typedef priority_queue<vl, vector<vl>, greater<vl >> vlgreaterq;
#define bit(x,v) ((ll)x << v)
#define rep(x,v) for(ll x=0;x<v;x++)
#define rep2(x,f,v) for(ll x=f;x<v;x++)
// 許容する誤差ε
#define EPS (1e-10)
// 2つのスカラーが等しいかどうか
#define EQ(a,b) (std::abs((a)-(b)) < EPS)
// 2つのベクトルが等しいかどうか
#define EQV(a,b) ( EQ((a).real(), (b).real()) && EQ((a).imag(), (b).imag()) )
#define all(a) a.begin(),a.end()
#define all0(a) memset(a,0,sizeof(a))
const ll INF = 1000000007;
const int MAX = 2000010;
const int MOD = 1000000007;

long long fac[MAX], finv[MAX], inv[MAX];
void COMinit() {
	fac[0] = fac[1] = 1;
	finv[0] = finv[1] = 1;
	inv[1] = 1;
	for (int i = 2; i < MAX; i++) {
		fac[i] = fac[i - 1] * i % MOD;
		inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
		finv[i] = finv[i - 1] * inv[i] % MOD;
	}
}

// 二項係数計算
long long COM(int n, int k) {
	if (n < k) return 0;
	if (n < 0 || k < 0) return 0;
	return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}

ll gcd(ll a, ll b) {
	if (b == 0) return a;
	return gcd(b, a % b);
}
int pr[200010];
int lank[200010];
void uini(int n) {
	for (size_t i = 0; i <= n; i++)
	{
		pr[i] = i;
	}
}

int parent(int x) {
	if (x == pr[x]) return x;
	return pr[x] = parent(pr[x]);
}

int same(int x, int y) {
	return parent(x) == parent(y);
}

bool unit(int x, int y) {
	int px = parent(x);
	int py = parent(y);

	if (px == py) return false;
	if (lank[px] < lank[py]) {
		pr[py] = px;
		lank[px] += lank[py] + 1;
	}
	else {
		pr[px] = py;
		lank[py] += lank[px] + 1;
	}
	return true;
}

ll bit[200010];
int max_n = 200000;
int pm = 0;
void add(int x) {

	while (max_n >= x)
	{
		bit[x]++;
		x += x & -x;
	}
}
void sub(int x) {
	while (max_n >= x)
	{
		bit[x]--;
		x += x & -x;
	}
}
ll merge(ll* a, int left, int mid, int right) {
	ll n1 = mid - left;
	ll n2 = right - mid;
	vector<int> L(n1 + 1);
	vector<int> R(n2 + 1);
	for (size_t i = 0; i < n1; i++)
	{
		L[i] = a[left + i];
	}
	for (size_t i = 0; i < n2; i++)
	{
		R[i] = a[mid + i];
	}

	L[n1] = INF;
	R[n2] = INF;
	ll i = 0;
	ll j = 0;
	ll r = 0;
	for (size_t k = left; k < right; k++)
	{
		if (L[i] <= R[j]) {
			a[k] = L[i];
			i++;
		}
		else {
			a[k] = R[j];
			r += n1 - i;
			j++;
		}
	}
	return r;
}
ll merge2(pair<int, char>* a, int left, int mid, int right) {
	ll n1 = mid - left;
	ll n2 = right - mid;
	vector<pair<int, char>> L(n1 + 1);
	vector<pair<int, char>> R(n2 + 1);
	for (size_t i = 0; i < n1; i++)
	{
		L[i] = a[left + i];
	}
	for (size_t i = 0; i < n2; i++)
	{
		R[i] = a[mid + i];
	}

	L[n1] = make_pair(INF, ' ');
	R[n2] = make_pair(INF, ' ');
	ll i = 0;
	ll j = 0;
	ll r = 0;
	for (size_t k = left; k < right; k++)
	{
		if (L[i].first <= R[j].first) {
			a[k] = L[i];
			i++;
		}
		else {
			a[k] = R[j];
			r += n1 - i;
			j++;
		}
	}
	return r;
}
ll mergeSort2(pair<int, char>* a, int left, int right) {
	ll res = 0;
	if (left + 1 < right) {
		int mid = (left + right) / 2;
		res = mergeSort2(a, left, mid);
		res += mergeSort2(a, mid, right);
		res += merge2(a, left, mid, right);
	}
	return res;
}
ll mergeSort(ll* a, int left, int right) {
	ll res = 0;
	if (left + 1 < right) {
		int mid = (left + right) / 2;
		res = mergeSort(a, left, mid);
		res += mergeSort(a, mid, right);
		res += merge(a, left, mid, right);
	}
	return res;
}
int partition(pair<int, char>* a, int p, int r) {
	pair<int, char> x = a[r];
	int i = p - 1;
	for (size_t j = p; j < r; j++)
	{
		if (a[j].first <= x.first) {
			i++;
			swap(a[i], a[j]);
		}
	}
	swap(a[i + 1], a[r]);
	return i + 1;
}
void quick(pair<int, char>* a, int p, int r) {
	if (p < r) {
		int q = partition(a, p, r);
		quick(a, p, q - 1);
		quick(a, q + 1, r);
	}
}

ll n;
int ci = 0;
ll P[1000010];
struct Node {
	int key;
	int priority;
	Node* parent, * left, * right;
	Node(int key, int priority);
	Node() {}
};
Node NIL;
Node::Node(int key, int priority) : key(key), priority(priority) {
	left = &NIL;
	right = &NIL;
}
Node* root = new Node();
void cenrec(Node* k) {
	if (k->key == NIL.key) return;
	cenrec(k->left);
	cout << " " << k->key;
	cenrec(k->right);
}
void fastrec(Node* k)
{
	if (k->key == NIL.key) return;
	cout << " " << k->key;
	fastrec(k->left);
	fastrec(k->right);
}
void insert(Node* v) {
	Node* y = &NIL;
	Node* x = root;
	while (x->key != NIL.key)
	{
		y = x;
		if (v->key < x->key) {
			x = x->left;
		}
		else {
			x = x->right;
		}
	}
	v->parent = y;
	if (y->key == NIL.key) {
		root = v;
	}
	else if (v->key < y->key) {
		y->left = v;
	}
	else {
		y->right = v;
	}

}

Node* find(Node* k, ll v)
{
	if (k->key == NIL.key) return &NIL;
	if (k->key == v) return k;
	if (v < k->key) return find(k->left, v);
	return find(k->right, v);
}
void delp12(Node* x) {
	if (x->key == NIL.key)  return;
	Node* l = x->left;
	Node* r = x->right;
	Node* pr = x->parent;

	if (l->key == NIL.key
		&& r->key == NIL.key) {
		if (pr->left == x) {
			pr->left = &NIL;
		}
		else pr->right = &NIL;
	}
	else if (l->key != NIL.key) {
		if (pr->left == x) {
			pr->left = l;
		}
		else pr->right = l;
		l->parent = pr;
	}
	else if (r->key != NIL.key) {
		if (pr->left == x) {
			pr->left = r;
		}
		else pr->right = r;
		r->parent = pr;
	}
}
Node* get_next(Node* k) {
	if (k->key == NIL.key) return &NIL;
	Node* res = get_next(k->left);
	if (res->key != NIL.key) return res;
	return k;
}
void del(Node* x) {

	if (x->key == NIL.key) return;
	Node* l = x->left;
	Node* r = x->right;
	Node* pr = x->parent;

	if (l->key != NIL.key && r->key != NIL.key) {
		Node* nex = get_next(r);
		x->key = nex->key;
		delp12(nex);
	}
	else {
		delp12(x);
	}
}
Node* rightRotate(Node* t) {
	Node* s = t->left;
	t->left = s->right;
	s->right = t;
	return s;
}
Node* leftRotate(Node* t) {
	Node* s = t->right;
	t->right = s->left;
	s->left = t;
	return s;
}
Node* _insert(Node* t, int key, int priority) {
	if (t->key == NIL.key) {
		return new Node(key, priority);
	}
	if (key == t->key) {
		return t;
	}

	if (key < t->key) {
		t->left = _insert(t->left, key, priority);
		if (t->priority < t->left->priority) {
			t = rightRotate(t);
		}
	}
	else {
		t->right = _insert(t->right, key, priority);
		if (t->priority < t->right->priority) {
			t = leftRotate(t);
		}
	}
	return t;
}
Node* delete1(Node* t, int key);
Node* _delete(Node* t, int key) {
	if (t->left->key == NIL.key && t->right->key == NIL.key) {
		return &NIL;
	}
	else if (t->left->key == NIL.key) {
		t = leftRotate(t);
	}
	else if (t->right->key == NIL.key) {
		t = rightRotate(t);
	}
	else
	{
		if (t->left->priority > t->right->priority) {
			t = rightRotate(t);
		}
		else
			t = leftRotate(t);
	}
	return delete1(t, key);
}
Node* delete1(Node* t, int key) {
	if (t->key == NIL.key) {
		return &NIL;
	}
	if (key < t->key) {
		t->left = delete1(t->left, key);
	}
	else if (key > t->key) {
		t->right = delete1(t->right, key);
	}
	else return _delete(t, key);
	return t;
}
int H;
int left(int i) {
	return i * 2 + 1;
}
int right(int i) {
	return i * 2 + 2;
}


ll heap[2000010];
void maxHeapify(int i) {
	int l = left(i);
	int r = right(i);
	int largest = 0;
	if (l < H && heap[l] > heap[i])
		largest = l;
	else
		largest = i;
	if (r < H && heap[r] > heap[largest])
		largest = r;

	if (largest != i) {
		swap(heap[i], heap[largest]);
		maxHeapify(largest);
	}
}
int pare(int i) {
	return (i - 1) / 2;
}
void raise(int i) {
	int l = pare(i);
	if (l < 0) return;

	if (heap[l] < heap[i]) {
		swap(heap[i], heap[l]);
		raise(l);
	}
}
void minHeapify(int i) {
	int l = left(i);
	int r = right(i);
	int minimam = 0;
	if (l < H && heap[l] < heap[i])
		minimam = l;
	else
		minimam = i;
	if (r < H && heap[r] < heap[minimam])
		minimam = r;

	if (minimam != i) {
		swap(heap[i], heap[minimam]);
		minHeapify(minimam);
	}
}
void buildMaxHeap() {
	for (int i = H / 2; i >= 0; i--)
	{
		maxHeapify(i);
	}
}

int dx[] = { -1,0,1,0 };
int dy[] = { 0,-1,0,1 };
std::vector<int> find_all(const std::string str, const std::string subStr) {
	std::vector<int> result;

	int subStrSize = subStr.size();
	int pos = str.find(subStr);

	while (pos != std::string::npos) {
		result.push_back(pos);
		pos = str.find(subStr, pos + 1);
	}

	return result;
}
//ll memo[100010];
//ll next[100010];
//ll dm[100010];
//int f[100010];
//ll rec(int x) {
//
//	if (~memo[x]) return memo[x];
//	if (x == n) { 
//		dm[n] = 1;
//		return 1; 
//	}
//	ll *res = &memo[x];
//	*res = 0;
//	set<int> st;
//	st.insert(f[x]);
//	for (int i = x + 1; i <= n; i++)
//	{
//		if (~memo[i]) {
//			*res += memo[i] + 1;
//			*res %= INF;
//			break;
//		}
//
//		*res += rec(i);
//		*res %= INF;
//		if (st.find(f[i]) != st.end()) {break; }
//		st.insert(f[i]);
//	}
//
//	return *res;
//}
#define bit(x,v) ((ll)x << v)

class BIT {

	static const int MAX_N = 1000010;
public:
	BIT() { memset(bit, 0, sizeof(bit)); }
	int bit[MAX_N + 1], n;
	int sum(int i) {
		int s = 0;
		while (i > 0)
		{
			s += bit[i];
			i -= i & -i;
		}
		return s;
	}

	void add(int i, int x) {
		while (i <= n)
		{
			bit[i] += x;
			i += i & -i;
		}
	}
	void clear() {
		memset(bit, 0, sizeof(bit));
	}
	int a[MAX_N];
	void bable_swap_count() {
		ll ans = 0;
		for (size_t j = 0; j < n; j++)
		{
			ans += j - sum(a[j]);
			add(a[j], 1);
		}
		printf("%lld\n", ans);
	}

	int search(int s, int x) {

		ll half = (s + x) / 2;
		ll sh = sum(x);

		ll sl = sum(half);

		ll st = sum(s);
		if (sh - sl == 0) {
			return x;
		}
		if (sh - sl < x - half) {
			return search(half, x);
		}

		if (sl - st == 0) {
			return half;
		}

		if (sl - st < half - s) {
			return search(s, half);
		}
		return -1;
	}

	int lankSearch(int lank) {
		return lankSearch(lank, 0, MAX_N);
	}
	int lankSearch(int lank, int s, int t) {

		ll half = (s + t) / 2;

		ll v = sum(half);
		ll v1 = sum(t);
		ll v2 = sum(s);
		if (lank == 1) {
			if (s + 1 >= t) return t;
			else if (v - v2 > 0) {
				return lankSearch(lank, s, half);
			}
			else return lankSearch(lank, half, t);
		}

		if ((v - v2) < lank) {
			return lankSearch(lank - (v - v2), half, t);
		}
		if ((v - v2) >= lank) {
			return lankSearch(lank, s, half);
		}

		return -1;
	}
};

class BIT2 {

	static const int MAX_N = 1000010;
public:
	BIT2() { memset(bit, 0, sizeof(bit)); }
	ll bit[MAX_N + 1], n;
	ll gmax(int i) {
		ll s = 0;
		while (i > 0)
		{
			s = max(bit[i], s);
			i -= i & -i;
		}
		return s;
	}

	void add(int i, ll x) {
		while (i <= n)
		{
			bit[i] = max(bit[i], x);
			i += i & -i;
		}
	}
	void clear() {
		memset(bit, 0, sizeof(bit));
	}

};
vector<ll> getp(ll n) {

	vector<ll> res;
	ll a = 2;
	if (n % 2 == 0) {
		res.push_back(2);
		while (n % 2 == 0)n /= 2;
	}

	for (ll i = 3; i * i <= n; i += 2)
	{
		if (n % i == 0) {
			res.push_back(i);
			while (n % i == 0)n /= i;
		}
	}
	if (n != 1) res.push_back(n);
	return res;
}
vector<ll> getp2(ll n) {

	vector<ll> res;
	ll a = 2;
	if (n % 2 == 0) {

		while (n % 2 == 0) { n /= 2; res.push_back(2); }
	}

	for (ll i = 3; i * i <= n; i += 2)
	{
		if (n % i == 0) {

			while (n % i == 0) { n /= i; res.push_back(i); }
		}
	}
	if (n != 1) res.push_back(n);
	return res;
}
vector<pll> getp3(ll n) {

	vector<pll> res;
	ll a = 2;
	int cnt = 0;
	if (n % 2 == 0) {
		res.push_back(make_pair(2, 0));
		while (n % 2 == 0) { n /= 2; res[cnt].second++; }
		cnt++;
	}

	for (ll i = 3; i * i <= n; i += 2)
	{
		if (n % i == 0) {
			res.push_back(make_pair(i, 0));
			while (n % i == 0) { n /= i; res[cnt].second++; }
			cnt++;
		}
	}
	if (n != 1) res.push_back(make_pair(n, 1));
	return res;
}
vector<ll> getDivisors(ll n) {

	vector<ll> res;
	ll a = 2;
	res.push_back(1);
	for (ll i = 2; i * i <= n; i++)
	{

		if (n % i == 0) {
			res.push_back(i);
			if (n / i != i)
				res.push_back(n / i);
		}
	}
	return res;
}

struct ve {
public:
	vector<ve> child;
	int _t = INF;
	ve(int t) :_t(t) {}
	ve(ve _left, ve _right) {
		_t = _left._t + _right._t;
		child.push_back(_left);
		child.push_back(_right);
	}
	bool operator<(const ve& t) const {
		return _t > t._t;
	}
};

vector<bool> elas(ll n) {
	vector<bool> r(n);
	for (ll i = 3; i < n; i += 2)
	{
		r[i] = 1;
	}
	r[0] = 0;
	r[1] = 0;
	r[2] = 1;
	for (ll i = 3; i * i < n; i += 2)
	{
		if (!r[i]) continue;
		ll ti = i * 2;
		while (ti < n)
		{
			r[ti] = false;
			ti += i;
		}
	}
	return r;
}
bool isprime(ll v) {
	for (ll i = 2; i * i <= v; i++)
	{
		if (v % i == 0) return false;
	}
	return true;
}

ll lcm(vector<ll> v) {
	if (v.size() == 0) return 0;
	ll t = v[0];
	for (size_t i = 1; i < v.size(); i++)
	{
		t = v[i] * t / gcd(v[i], t);
	}
	return t;
}
ll eulerphi(ll n) {
	auto p = getp(n);
	double u = n;
	for (auto v : p) {
		u *= (double)(v - 1) / (double)v;
	}
	return u;
}

double revs(double x) {
	ll dig = 0;
	stringstream st;
	st << std::fixed << setprecision(0) << x;
	string v = st.str();
	reverse(v.begin(), v.end());
	return stod(v);
}
bool chkparindrome(double x) {
	stringstream st;
	st << std::fixed << setprecision(0) << x;
	string p = st.str();
	for (size_t i = 0; i < p.size() / 2; i++)
	{
		if (p[i] != p[p.size() - i - 1]) {
			return false;
		}
	}
	return true;
}
ll digitC(double x) {
	stringstream st;
	st << fixed << setprecision(0) << x;
	return st.str().size();
}
ll digitSum(double x) {
	stringstream st;
	st << std::fixed << x;
	string p = st.str();
	ll rs = 0;
	for (size_t i = 0; i < p.size(); i++)
	{
		if (p[i] == '.') break;
		rs += p[i] - '0';
	}
	return rs;
}
pdd recs(int x) {

	if (x == 0) return make_pair(1, 2);
	pdd d = recs(x - 1);
	auto nu = d.second * 2.0 + d.first;
	auto de = d.second;
	return make_pair(de, nu);
}
ll caldig(ll a) {
	ll r = 0;
	while (a > 0) { a /= 10; r++; }
	return r;
}
int chav(char v) {
	if (v <= 'Z') return v - 'A';
	return v - 'a' + 26;
}
char itoch(int i) {
	if (i < 26) return i + 'A';
	return (i - 26) + 'a';
}
int crmp[1000][1000];
int countR(ll base, ll x, ll y, int deep) {

	if (~crmp[x][y]) {
		return deep - crmp[x][y];
	}
	crmp[x][y] = deep;
	double nu = sqrt(base) + x;
	double de = (base - (x * x)) / y;
	ll u = nu / de;
	ll nx = x - (u * de);
	return countR(base, -nx, de, deep + 1);
}

bool isPermutation(ll x, ll y) {
	int c1[10];
	int c2[10];
	memset(c1, 0, sizeof(c1));
	memset(c2, 0, sizeof(c2));
	while (x > 0)
	{
		c1[x % 10]++;
		x /= 10;
	}
	while (y > 0)
	{
		c2[y % 10]++;
		y /= 10;
	}

	for (size_t i = 0; i < 10; i++)
	{
		if (c1[i] != c2[i]) return false;
	}
	return true;
}

double heron(ll a, ll b, ll c) {
	double s = (double)(a + b + c) / 2.0;
	return sqrt(s * (s - a) * (s - b) * (s - c));
}

double calcThreePS(double x1, double y1, double x2, double y2, double x3, double y3) {
	return abs((x1 * y2 + x2 * y3 + x3 * y1 - y1 * x2 - y2 * x3 - y3 * x1) / 2.0);
}
typedef vector<vl> mat;
class Matrix1 {

public:
	static const int M = INF;
	int n;
	mat mul(mat& A, mat& B) {
		mat C(A.size(), vl(B[0].size()));
		for (size_t i = 0; i < A.size(); i++)
		{
			for (size_t k = 0; k < B.size(); k++)
			{
				for (size_t j = 0; j < B[0].size(); j++)
				{
					C[i][j] = (C[i][j] + A[i][k] * B[k][j]) % M;
				}
			}
		}
		return C;
	}

	mat pow(mat A, ll n) {
		mat B(A.size(), vl(A.size()));
		for (size_t i = 0; i < A.size(); i++)
		{
			B[i][i] = 1;
		}
		while (n > 0) {
			if (n & 1) B = mul(B, A);
			A = mul(A, A);
			n >>= 1;
		}


		return B;
	}

};
ll m;
ll stringDivRm(string s, ll k) {

	ll v = 0;
	
	for (size_t i = 0; i < s.size(); i++)
	{
		v *= 10;
		v += s[i] - '0';
		v %= k;
	}
	return v;
}

ll repPow(ll b, ll x,ll md) {
	ll res = 1;
	ll v = b;

	while (x > 0)
	{
		if (x & 1) {
			res *= v;
			res %= md;
		}
		v *= v;
		v %= md;
		x >>= 1;
	}

	return res;
}
ll repPow(ll b, ll x) {
	return repPow(b, x, INF);
}
ll uar[1000010];
ll upr(ll u, ll r) {
	return (fac[u] * finv[u-r]) % INF;
}
ll partitionMemo[20010][110];
ll partitionNum(ll v, ll k) {
	if (k == 1) return 1;
	if (v <= 1) return 1;
	if (~partitionMemo[v][k]) return partitionMemo[v][k];
	ll r = 0;
	if (v < k) {
		r = partitionNum(v,v);
	}
	else
		r = partitionNum(v, k - 1) + partitionNum(v - k, k);
	r %= INF;

	return partitionMemo[v][k] = r;
}

class SetTree1 {

public:
	static const int MAX_N = 100000;
	static const int MAX_Q = 100000;
	int N, Q;
	static const int DAT_SIZE = (1 << 18) - 1;
	int A[MAX_N];
	char T[MAX_Q];

	ll data[DAT_SIZE];
	void init(int _n) {
		memset(data, 0, sizeof(data));
		int p = 1;
		while (p < _n)
		{
			p <<= 1;
		}
		N = p;
		Q = N - 1;
	}
	void update(int a, int b) {

		for (size_t i = a; i <= b; i++)
		{
			update(Q + i);
		}
	}
	void update(int a) {

		int x = data[a];
		while (a > 0)
		{
			if (a % 2 == 0)a--;
			a >>= 1;
			data[a] += x;
		}
	}
	void add(int a, int b, int x) {
		add(a, b + 1, x, 0,0,N);
	}
	void add(int a, int b, int x, int k, int l, int r) {
		if (a <= l && r <= b) {
			data[k] += x;
		}
		else if (l < b && a < r) {
			data[k] += (min(b, r) - max(a, l)) * x;
			add(a, b, x, k * 2 + 1, l, (l + r) / 2);
			add(a, b, x, k * 2 + 2, (l + r) / 2, r);
		}
	}
	ll sum(int a, int b) {
		return sum(a, b + 1, 0, 0, N);
	}
	ll sum(int a, int b, int k, int l, int r) {
		if (b <= l || r <= a) return 0;
		else if (a <= l && r <= b) {
			return data[k];
		}
		else {
			ll res = 0;
			res += sum(a, b, k * 2 + 1, l, (l + r) / 2);
			res += sum(a, b, k * 2 + 2, (l + r) / 2, r);
			return res;
		}
	}

};
class Segment;
class Circle;
class Point {
public:
	double x, y;

	Point(double x = 0, double y = 0) :x(x), y(y) {}

	Point operator + (Point p) { return Point(x + p.x, y + p.y); }
	Point operator - (Point p) { return Point(x - p.x, y - p.y); }
	Point operator * (double a) { return Point(a * x, a * y); }
	Point operator / (double a) { return Point(x / a, y / a); }

	double abs() { return sqrt(norm()); }
	double norm() { return x * x + y * y; }

	bool operator < (const Point& p)const {
		return x != p.x ? x < p.x : y < p.y;
	}
	bool operator == (const Point& p) const {
		return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;
	}
	static double dot(Point a, Point b) {
		return a.x * b.x + a.y * b.y;
	}
	static double cross(Point a, Point b) {
		return a.x * b.y - a.y * b.x;
	}
	static bool isOrthogonal(Point a, Point b) {
		return EQ(dot(a, b), 0.0);
	}
	static bool isOrthogonal(Point a1, Point a2, Point b1, Point b2) {
		return isOrthogonal(a1 - a2, b1 - b2);
	}
	static bool isOrthogonal(Segment s1, Segment s2);

	static bool isPalallel(Point a, Point b) {
		return EQ(cross(a, b), 0.0);
	}
	static bool isPalallel(Point a1, Point a2, Point b1, Point b2) {
		return isPalallel(a1 - a2, b1 - b2);
	}
	static bool isPalallel(Segment s1, Segment s2);

	static const int COUNTER_CLOCKWISE = 1;
	static const int CLOCKWISE = -1;
	static const int ONLINE_BACK = 2;
	static const int ONLINE_FRONT = -2;
	static const int ON_SEGMENT = 0;
	static int ccw(Point p0, Point p1, Point p2) {
		Point a = p1 - p0;
		Point b = p2 - p0;
		if (cross(a, b) > EPS) return COUNTER_CLOCKWISE;
		if (cross(a, b) < -EPS) return CLOCKWISE;
		if (dot(a, b) < -EPS) return ONLINE_BACK;
		if (a.norm() < b.norm()) return ONLINE_FRONT;
		return ON_SEGMENT;
	}

	static bool intersect(Point p1, Point p2, Point p3, Point p4) {
		return (ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0
			&& ccw(p3, p4, p1) * ccw(p3, p4, p2) <= 0);
	}
	static bool intersect(Segment s1, Segment s2);
	static Point project(Segment s, Point p);

	static Point reflect(Segment s, Point p);

	static Point getDistance(Point a, Point b) {
		return (a - b).abs();
	}

	static double getDistanceLP(Segment s, Point p);

	static double getDistanceSP(Segment s, Point p);

	static double getDistance(Segment s1, Segment s2);

	static Point getIntersection(Segment s1, Segment s2);

	static pair<Point, Point> crossPoints(Circle c, Segment s);

	static int contains(vector<Point> g, Point p) {
		int n = g.size();
		bool x = false;
		rep(i, n) {
			Point a = g[i] - p, b = g[(i + 1) % n] - p;
			// 線の上に載っているか
			if (std::abs(cross(a, b)) < EPS && dot(a, b) < EPS) return 1;

			// pを基準として上下にあるか
			// または外積が正か?(→にあるか)
			if (a.y > b.y) swap(a, b);
			if (a.y < EPS && EPS < b.y && cross(a, b) > EPS) x = !x;
		}
		return x ? 2 : 0;
	}

	static vector<Point> andrewScan(vector<Point> s) {
		vector<Point> u, l;
		if (s.size() < 3) return s;
		sort(all(s));
		u.push_back(s[0]);
		u.push_back(s[1]);
		l.push_back(s[s.size() - 1]);
		l.push_back(s[s.size() - 2]);

		for (int i = 2; i < s.size(); i++) {

			for (int _n = u.size(); _n >= 2 && ccw(u[_n - 2], u[_n - 1], s[i]) > CLOCKWISE; _n--) {
				u.pop_back();
			}
			u.push_back(s[i]);
		}

		for (int i = s.size() - 3; i >= 0; i--) {

			for (int _n = l.size(); _n >= 2 && ccw(l[_n - 2], l[_n - 1], s[i]) > CLOCKWISE; _n--) {
				l.pop_back();
			}
			l.push_back(s[i]);
		}

		reverse(all(l));
		for (int i = u.size() - 2; i >= 1; i--)
		{
			l.push_back(u[i]);
		}

		return l;
	}

	static double getArea(vector<Point> g) {
		double res = 0;
		rep(i, n) {
			int ne = (i + 1) % n;
			res += cross(g[i], g[ne]);
		}
		return res / 2.0;
	}
};

class Segment {
public:
	Point p1, p2;
	Segment() {}
	Segment(Point p1, Point p2) :p1(p1), p2(p2) {}
	Point p1tp2() { return p2 - p1; }
	Point p2tp1() { return p1 - p2; }
	double norm() {
		return (p2 - p1).norm();
	}
	void getCin() {
		cin >> p1.x >> p1.y >> p2.x >> p2.y;
	}
};

bool Point::isOrthogonal(Segment s1, Segment s2) {
	return EQ(dot(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}
bool Point::isPalallel(Segment s1, Segment s2) {
	return EQ(cross(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}
bool Point::intersect(Segment s1, Segment s2) {
	return intersect(s1.p1, s1.p2, s2.p1, s2.p2);
}
Point Point::project(Segment s, Point p) {
	Point base = s.p2 - s.p1;
	double r = Point::dot(p - s.p1, base) / base.norm();
	return s.p1 + base * r;
}
Point Point::reflect(Segment s, Point p) {
	return (project(s, p) * 2) - p;
}
double Point::getDistanceLP(Segment s, Point p) {
	return std::abs(cross(s.p2 - s.p1, p - s.p1) / (s.p2 - s.p1).abs());
}
double Point::getDistanceSP(Segment s, Point p) {
	if (dot(s.p2 - s.p1, p - s.p1) < 0.0) return (p - s.p1).abs();
	if (dot(s.p1 - s.p2, p - s.p2) < 0.0) return (p - s.p2).abs();
	return getDistanceLP(s, p);
}
double Point::getDistance(Segment s1, Segment s2) {
	if (intersect(s1, s2)) return 0.0;
	return min({ getDistanceSP(s1,s2.p1),getDistanceSP(s1,s2.p2)
		,getDistanceSP(s2,s1.p1),getDistanceSP(s2,s1.p2) });
}
Point Point::getIntersection(Segment s1, Segment s2) {
	// (s1.p1 - s2.p1).norm()
	auto bs = s1.p2 - s1.p1;
	auto n1 = s2.p1 - s1.p1;
	auto n2 = s2.p2 - s1.p1;
	auto c1 = std::abs(cross(n1, bs)) / bs.norm();
	auto c2 = std::abs(cross(n2, bs)) / bs.norm();
	return s2.p1 + (s2.p2 - s2.p1) * (c1 / (c1 + c2));
	// c1:c2=t:1-t
	// c2t=(1-t)c1
	// t/(1-t)=c1/(c1+c2)
	// 
}


double arg(Point p) { return atan2(p.y, p.x); }
Point polar(double a, double r) { return Point(cos(r) * a, sin(r) * a); }
class Circle {
public:
	Point c;
	double r;
	Circle(Point c = Point(), double r = 0.0) : c(c), r(r) {}
	static pair<Point, Point> getCrossPoints(Circle c1, Circle c2) {
		double d = (c1.c - c2.c).abs(); // 中心点どうしの距離
		double a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d));
		double t = arg(c2.c - c1.c);
		return make_pair(c1.c + polar(c1.r, t + a), c1.c + polar(c1.r, t - a));

	}
	void getCin() {
		cin >> c.x >> c.y >> r;
	}
};

pair<Point, Point> Point::crossPoints(Circle c, Segment s) {
	auto pp = project(s, c.c);
	auto f = (pp - c.c).norm();
	auto mu = sqrt(c.r * c.r - f);
	auto e = s.p1tp2() / s.p1tp2().abs();
	return make_pair(pp + e * mu, pp - e * mu);

}

ll count(vector<ll> v, ll x) {
	ll res = 0;
	ll si = v.size();
	rep(i, v.size()) {
		ll p = lower_bound(all(v), x / v[i] + (x % v[i] > 0 ? 1 : 0)) - v.begin();
		if (i < p) p--;
		res += max(p - i,0LL);
	}
	return res;
}
void solv() {
	Circle c;
	c.getCin();
	cin >> n;
	cout << fixed << setprecision(10);
	rep(i, n) {
		Segment s;
		s.getCin();
		// 円と直線の交点
		// 三角形を利用する
		// 円の中点と直線の写像を取る
		// 二つの交点がある場合、写像への距離は同じとなる
		// 距離を求める
		// 写像、交点、中点の関係は直角三角形となっている
		// 斜辺は半径rなので中点写像への距離xが分かれば
		// 求められる
		// ここで、単位ベクトルに長さを掛けるか
		// 直線のそれぞれの点から写像までの距離を求めて比率を掛ける方法がある
		auto p = Point::crossPoints(c, s);
		auto p1 = p.first;
		auto p2 = p.second;
		if (p1.x > p2.x || (p1.x == p2.x && p1.y > p2.y))swap(p1, p2);
		cout << p1.x << " " << p1.y << " " << p2.x << " " << p2.y << endl;;
	}
}
int main() {
	//COMinit();
	solv();
	return 0;
}
 


Measured memory_bytes: 3324