//#pragma GCC optimize("O3")
//#pragma GCC target("tune=native")
//#pragma GCC optimize("O3,unroll-loops")
//#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#include "game.h"
#include<iostream>
#include<vector>
#include<queue>
#include<deque>
#include<string>
#include<fstream>
#include<algorithm>
#include <iomanip>
#include<map>
#include <set>
#include <unordered_map>
#include <stack>
#include <unordered_set>
#include <cmath>
#include <cstdint>
#include <cassert>
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/tree_policy.hpp>
#define shit short int
#define ll long long
//#define int ll
#define For(i, n) for(int i = 0; i < (int)n; i++)
#define ffor(i, a, n) for(int i = (int)a; i < (int)n; i++)
#define rfor(i, n) for(int i = (int)n; i >= (int)0; i--)
#define rffor(i, a, n) for(int i = (int)n; i >= (int)a; i--)
#define vec vector
#define ff first
#define ss second
#define pb push_back
#define pii pair<int, int>
#define NEK 2000000000
#define mod 998244353
#define mod2 1000000009
#define rsz resize
#define prv1 43
#define prv2 47
#define D 8
#define trav(a,x) for (auto& a: x)
#define pb push_back
#define ub upper_bound
#define lb lower_bound
#define all(x) (x).begin(), (x).end()
#define sig 0.0000001
using namespace std;
//using namespace __gnu_pbds;
//template <typename T1, typename T2>
//using indexed_set = tree<pair<T1, T2>, null_type, less<pair<T1, T2>>, rb_tree_tag, tree_order_statistics_node_update>;
ll nsd(ll a, ll b) {
	while (b) {
		a %= b;
		swap(a, b);
	}
	return a;
}
class treap {
	struct node {
		node* l = nullptr;
		node *r = nullptr;
		ll val, nsd;
		int key, priority, key2;
		node(ll val1, int key1, int key12) {
			val = val1, key = key1;
			key2 = key12;
			priority = rand();
			nsd = val1;
		}
	};
	typedef node* pnode;
	pnode root = nullptr;
	ll get_nsd(pnode t) {
		if (!t) return 0;
		return t->nsd;
	}
	void update(pnode t) {
		if (!t) return;
		t->nsd = nsd(nsd(get_nsd(t->l), get_nsd(t->r)), t->val);
		return;
	}
	bool porovnaj(int a1, int a2, int b1, int b2) {
		if (a1 == b1) {
			return a2 > b2;
		}
		return a1 > b1;
	}
	void split(pnode t, int key, int key2, pnode& l, pnode& r) {
		if (!t) {
			l = r = nullptr;
			return;
		}
		if (porovnaj(t->key, t->key2, key, key2)) {
			split(t->l, key, key2, l, t->l);
			r = t;
		}
		else {
			split(t->r, key, key2, t->r, r);
			l = t;
		}
		update(t);
		return;
	}
	void merge(pnode& t, pnode l, pnode r) {
		if (!l || !r) {
			t = l ? l : r;
			return;
		}
		if (l->priority > r->priority) {
			merge(l->r, l->r, r);
			t = l;
		}
		else {
			merge(r->l, l, r->l);
			t = r;
		}
		update(t);
		return;
	}
	void insert(pnode& t, pnode x) {
		if (!t) {
			t = x;
			return;
		}
		if (x->priority > t->priority) {
			split(t, x->key, x->key2, x->l, x->r);
			t = x;
		}
		else {
			insert(porovnaj(t->key, t->key2, x->key, x->key2) ? t->l : t->r, x);
		}
		update(t);
		return;
	}
	void erase(pnode& t, int key, int key2) {
		if (!t) return;
		if (t->key == key && t->key2 == key2) {
			merge(t, t->l, t->r);
		}
		else {
			erase(porovnaj(t->key, t->key2, key, key2) ? t->l : t->r, key, key2);
		}
		update(t);
		return;
	}
public:
	void zmen(int key2, int key, ll val) {
		erase(root, key, key2);
		insert(root, new node(val, key, key2));
		return;
	}
	ll daj(int a, int b) {
		pnode l, r;
		l = r = nullptr;
		split(root, a, (-1) * NEK, root, r);
		split(r, b+1, (-1) * NEK, l, r);
		ll odp = get_nsd(l);
		merge(root, root, l);
		merge(root, root, r);
		return odp;
	}
};
class intervalac {
	int n;
	struct node {
		node* l = nullptr;
		node* r = nullptr;
		treap in;
	};
	typedef node* pnode;
	pnode root = new node;
	void propagate(pnode t) {
		if (!t->l) t->l = new node;
		if (!t->r) t->r = new node;
		return;
	}
	void zmen(pnode t, int l, int r, int a, int b, ll k) {
		if (a > r || a < l) return;
		t->in.zmen(a, b, k);
		if (r == l) return;
		propagate(t);
		int m = (l + r) / 2;
		zmen(t->l, l, m, a, b, k); zmen(t->r, m + 1, r, a, b, k);
		return;
	}
	ll daj(pnode t, int l, int r, int a, int b, int c, int d) {
		if (a > r || b < l) return 0;
		if (a <= l && r <= b) {
			return t->in.daj(c, d);
		}
		propagate(t);
		int m = (l + r) / 2;
		return nsd(daj(t->l, l, m, a, b, c, d), daj(t->r, m + 1, r, a, b, c, d));
	}
public:
	void postav(int vel) {
		n = vel;
		return;
	}
	void zmen(int p, int q, ll k) {
		zmen(root, 0, n - 1, p, q, k);
		return;
	}
	ll daj(int p, int q, int u, int v) {
		return daj(root, 0, n - 1, p, q, u, v);
	}
};
intervalac seg;
void init(int r2, int c2) {
	int r = r2, c = c2;
	seg.postav(r);
	return;
}
void update(int p, int q, ll k) {
	seg.zmen(p, q, k);
	return;
}
ll calculate(int p, int q, int u, int v) {
	return seg.daj(p, u, q, v);
}
/*
signed main() {
	ios_base::sync_with_stdio(false); cin.tie(NULL);
	int r, c, q; cin >> r >> c >> q;
	init(r, c);
	For(i, q) {
		int t; cin >> t;
		if (t == 1) {
			int p, q; ll k; cin >> p >> q >> k;
			update(p, q, k);
		}
		if (t == 2) {
			ll p, q, u, v; cin >> p >> q >> u >> v;
			cout << calculate(p, q, u, v) << '\n';
		}
	}
	return 0;
}*/
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