#include "gap.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i, n) for(int i = 1; (i) <= (n); ++i)
#define forn(i, l, r) for(int i = (l); i <= (r); ++i)
#define ford(i, r, l) for(int i = (r); i >= (l); --i)
#define FOR(i, n) for(int i = 0; i < (n); ++i)
#define FORD(i, n) for(int i = ((n) - 1); i >= 0; --i)
#define fi first
#define se second
#define pii pair<int, int>
#define pll pair<ll, ll>
#define pb push_back
#define endl "\n"
#define task "firework"
#define sz(a) int(a.size())
#define C(x, y) make_pair(x, y)
#define all(a) (a).begin(), (a).end()
#define bit(i, mask) (mask >> i & 1)
template<typename T> bool maximize(T &res, const T &val) { if (res < val){ res = val; return true; }; return false; }
template<typename T> bool minimize(T &res, const T &val) { if (res > val){ res = val; return true; }; return false; }
inline int readInt() {char c;while(c=getchar(),c!='-'&&(c<'0'||c>'9'));bool sign=(c=='-');if(sign)c=getchar();int n=c-'0';while(c=getchar(),c>='0'&&c<='9')n=10*n+c-'0';return(!sign)?n:-n;}
inline ll readLong() {char c;while(c=getchar(),c!='-'&&(c<'0'||c>'9'));bool sign=(c=='-');if(sign)c=getchar();ll n=c-'0';while(c=getchar(),c>='0'&&c<='9')n=10*n+c-'0';return(!sign)?n:-n;}
inline string readString() {char c;while(c=getchar(),c==' '||c=='\n'||c=='\t');string s({c});while(c=getchar(),c!=EOF&&c!=' '&&c!='\n'&&c!='\t')s+=c;return s;}
static int subtask_num, N;
static long long A[100001];
static long long call_count;
void MinMax(long long, long long, long long*, long long*);
ll findGap(int T, int N)
{
vector<ll> a(N + 2);
if(T == 1)
{
int l = 1, r = N;
ll lb = 0, rb = 1e18;
while(l <= r)
{
ll x, y;
MinMax(lb, rb, &a[l], &a[r]);
lb = a[l++] + 1;
rb = a[r--] - 1;
}
ll res = 0;
rep(i, N - 1) maximize(res, a[i + 1] - a[i]);
return res;
}
ll x, y;
MinMax(0, 1e18, &x, &y);
a[1] = x, a[N] = y;
ll res = 0;
ll Min_step = (a[N] - a[1] - 1) / (N - 1) + 1;
if(N == 2) return a[N] - a[1];
for(ll i = a[1], pre = a[1]; i <= a[N]; i += Min_step + 1)
{
MinMax(i, i + Min_step, &x, &y);
if(x != -1) maximize(res, x - pre), pre = y;
}
return res;
}
