C++ STL: How does the distance() method work for a set/ multiset (stored internally as a self balancing tree)?

I’m working on the problem: Count smaller elements on right side using Set in C++ STL

The solution is to add each element to the set and then to count the elements on the left, the distance function is called.

This is the algo:

1. Traverse the array element from i=len-1 to 0 and insert every element in a set. 2. Find the first element that is lower than A[i] using lower_bound function. 3. Find the distance between above found element and the beginning of the set using distance function. 4. Store the distance in another array Lets say CountSmaller. 4. Print that array 

I’m having a hard time to visualize or understand how can distance function be used with a set like structure since internally, the set data is stored as a self balanced tree (Red Black Tree). Whats the concept of distance for a self balancing tree and how does calling distance() give us the count of smaller elements on the right side?

Do any programming language function calls internally call Operating system APIs?

To list directory content in Python we use os.listdir(), In Java we use Files.list(new File(dirName).toPath()). Like this we use a lot of functions calls, eg: For Network connectivity, Print in screen, Save to files.

In all operating systems do these all language-specific function calls ultimately call OS APIs (In Windows I think it will be Win32 APIs)?

ANything we can do without call OS APIs?

Distributing library which internally using COM library

I would like to create a dll library that will be loading in runtime. The library’ll be using internally COM objects with MTA flag. The library will be created in main thread.

So I have question: Where there is best place where can I call ‘CoInitializeEx’ and ‘CoUninitialize’ functions. In the my dll(init/deinit functions) or client should call directly these functions?

I prefer first option. I would like avoid public dependig on COMs. Client shouldn’t know I’m using COMs, but also I’d like avoid crashes when client unload my lib(then I call ‘CoUninitialize’ for my lib) and other libs(depend on COM) will be in undefined state.

Is it best practice to setup a VPN for remote users to use even if there are no services hosted internally?

I am curious as to when a VPN should be implemented in a workplace. VPNs of course provide privacy/security in general, but is there really a point in setting one up for a workplace if there are no services running on internal networks at the company?

I’ve used them when I need to access internal servers, but if everything is hosted by 3rd party services, is there a need for a VPN setup?

It seems like a waste of resources since users can still easily do their work without connecting so most will probably not choose to use it.

OpenVPN over stunnel not working when forwarded through router but working internally

I’m trying to set up OpenVPN over stunnel on my personal server.

openvpn is in tcp and connects fine outside of stunnel, even when connecting through a port forward on the router.

OpenVPN wrapped in stunnel works fine when not connecting through the port forward on the router, i.e. stunnel sends to internal IP address.

stunnel appears to be working fine when connecting through a forwarded port on the router, I set up an stunnel for SSH and that connects fine, I even left it in a while loop outputting to the console for a couple of minutes to see if if would fail.

However, when running openVPN over stunnel and through a port forward on the router the connection appear to set up but then drops and I can’t get web traffic.

I’ve been debugging this all day and any help would be hugely appreciated.

I get the following warnings in the OVPN log:

WARNING: 'link-mtu' is used inconsistently, local='link-mtu 1552', remote='link-mtu 1544' WARNING: 'cipher' is used inconsistently, local='cipher AES-256-GCM', remote='cipher BF-CBC' WARNING: 'auth' is used inconsistently, local='auth [null-digest]', remote='auth SHA1' WARNING: 'keysize' is used inconsistently, local='keysize 256', remote='keysize 128' 

stunnel settings server (included ssh test):

[openvpn] accept = 44444 connect = 127.0.0.1:1194 ciphers = DHE-RSA-AES256-SHA256  [sslssh] accept = 55555 connect = 127.0.0.1:22 

stunnel settings client:

[openvpn]

client = yes accept = 127.0.0.1:11194 connect = <my_ip>:44444 ;cert = /usr/local/etc/stunnel/cert.pem ;connect = 192.168.255.25:44444 ciphers = DHE-RSA-AES256-SHA256  [sslssh] client = yes accept  = 127.0.0.1:2222 connect = <my_IP>:55555 

client ovpn config:

remote localhost 11194 proto tcp remote-cert-tls server   client dev tun resolv-retry infinite keepalive 10 120 nobind comp-lzo verb 3 

server ovpn config :

port 1194 proto tcp dev tun  comp-lzo keepalive 10 120  persist-key persist-tun user nobody group nogroup  chroot /etc/openvpn/easy-rsa/keys/crl.jail crl-verify crl.pem  ca /etc/openvpn/easy-rsa/keys/ca.crt dh /etc/openvpn/easy-rsa/keys/dh2048.pem tls-auth /etc/openvpn/easy-rsa/keys/ta.key 0 key /etc/openvpn/easy-rsa/keys/server.key cert /etc/openvpn/easy-rsa/keys/server.crt  ifconfig-pool-persist /var/lib/openvpn/server.ipp client-config-dir /etc/openvpn/server.ccd status /var/log/openvpn/server.log verb 4 

full ovpn client log

2019-05-27 14:10:53 *Tunnelblick: openvpnstart starting OpenVPN *Tunnelblick: OS X 10.14.6; Tunnelblick 3.7.5a (build 5011); prior version 3.4.0 (build 4007) 2019-05-27 14:10:53 *Tunnelblick: Attempting connection with mikewarde_tcp_stunnel using shadow copy; Set nameserver = 769; monitoring connection 2019-05-27 14:10:53 *Tunnelblick: openvpnstart start mikewarde_tcp_stunnel.tblk 1337 769 0 1 0 1065264 -ptADGNWradsgnw 2.4.4-openssl-1.0.2o 2019-05-27 14:10:54 *Tunnelblick: openvpnstart log:      OpenVPN started successfully. Command used to start OpenVPN (one argument per displayed line):            /Applications/Tunnelblick.app/Contents/Resources/openvpn/openvpn-2.4.4-openssl-1.0.2o/openvpn           --daemon           --log           /Library/Application Support/Tunnelblick/Logs/-SUsers-Smikewarde-SLibrary-SApplication Support-STunnelblick-SConfigurations-Smikewarde_tcp_stunnel.tblk-SContents-SResources-Sconfig.ovpn.769_0_1_0_1065264.1337.openvpn.log           --cd           /Library/Application Support/Tunnelblick/Users/mikewarde/mikewarde_tcp_stunnel.tblk/Contents/Resources           --setenv           IV_GUI_VER           "net.tunnelblick.tunnelblick 5011 3.7.5a (build 5011)"           --verb           3           --config           /Library/Application Support/Tunnelblick/Users/mikewarde/mikewarde_tcp_stunnel.tblk/Contents/Resources/config.ovpn           --verb           3           --cd           /Library/Application Support/Tunnelblick/Users/mikewarde/mikewarde_tcp_stunnel.tblk/Contents/Resources           --management           127.0.0.1           1337           /Library/Application Support/Tunnelblick/fognhooiggkindigaihckcifckpilcfpnmgdikmh.mip           --management-query-passwords           --management-hold           --script-security           2           --up           /Applications/Tunnelblick.app/Contents/Resources/client.up.tunnelblick.sh -9 -d -f -m -w -ptADGNWradsgnw           --down           /Applications/Tunnelblick.app/Contents/Resources/client.down.tunnelblick.sh -9 -d -f -m -w -ptADGNWradsgnw  2019-05-27 14:10:54 *Tunnelblick: Established communication with OpenVPN 2019-05-27 14:10:54 OpenVPN 2.4.4 x86_64-apple-darwin [SSL (OpenSSL)] [LZO] [LZ4] [PKCS11] [MH/RECVDA] [AEAD] built on Mar 27 2018 2019-05-27 14:10:54 library versions: OpenSSL 1.0.2o  27 Mar 2018, LZO 2.10 2019-05-27 14:10:54 MANAGEMENT: TCP Socket listening on [AF_INET]127.0.0.1:1337 2019-05-27 14:10:54 Need hold release from management interface, waiting... 2019-05-27 14:10:54 MANAGEMENT: Client connected from [AF_INET]127.0.0.1:1337 2019-05-27 14:10:54 MANAGEMENT: CMD 'pid' 2019-05-27 14:10:54 MANAGEMENT: CMD 'state on' 2019-05-27 14:10:54 MANAGEMENT: CMD 'state' 2019-05-27 14:10:54 MANAGEMENT: CMD 'bytecount 1' 2019-05-27 14:10:54 MANAGEMENT: CMD 'hold release' 2019-05-27 14:10:54 NOTE: the current --script-security setting may allow this configuration to call user-defined scripts 2019-05-27 14:10:54 Outgoing Control Channel Authentication: Using 160 bit message hash 'SHA1' for HMAC authentication 2019-05-27 14:10:54 Incoming Control Channel Authentication: Using 160 bit message hash 'SHA1' for HMAC authentication 2019-05-27 14:10:54 MANAGEMENT: >STATE:1558962654,RESOLVE,,,,,, 2019-05-27 14:10:54 TCP/UDP: Preserving recently used remote address: [AF_INET]127.0.0.1:11194 2019-05-27 14:10:54 Socket Buffers: R=[131072->131072] S=[131072->131072] 2019-05-27 14:10:54 Attempting to establish TCP connection with [AF_INET]127.0.0.1:11194 [nonblock] 2019-05-27 14:10:54 MANAGEMENT: >STATE:1558962654,TCP_CONNECT,,,,,, 2019-05-27 14:10:55 TCP connection established with [AF_INET]127.0.0.1:11194 2019-05-27 14:10:55 TCP_CLIENT link local: (not bound) 2019-05-27 14:10:55 TCP_CLIENT link remote: [AF_INET]127.0.0.1:11194 2019-05-27 14:10:55 MANAGEMENT: >STATE:1558962655,WAIT,,,,,, 2019-05-27 14:10:55 MANAGEMENT: >STATE:1558962655,AUTH,,,,,, 2019-05-27 14:10:55 TLS: Initial packet from [AF_INET]127.0.0.1:11194, sid=c58c277c 5918dc12 2019-05-27 14:10:55 VERIFY OK: depth=1, C=US, ST=CA, L=San Francisco, O=TurnKey Linux, OU=OpenVPN, CN=server, name=openvpn, emailAddress=vpn@radged.com 2019-05-27 14:10:55 VERIFY KU OK 2019-05-27 14:10:55 Validating certificate extended key usage 2019-05-27 14:10:55 ++ Certificate has EKU (str) TLS Web Server Authentication, expects TLS Web Server Authentication 2019-05-27 14:10:55 VERIFY EKU OK 2019-05-27 14:10:55 VERIFY OK: depth=0, C=US, ST=CA, L=San Francisco, O=TurnKey Linux, OU=OpenVPN, CN=server, name=openvpn, emailAddress=vpn@radged.com 2019-05-27 14:10:55 Control Channel: TLSv1.2, cipher TLSv1/SSLv3 ECDHE-RSA-AES256-GCM-SHA384, 2048 bit RSA 2019-05-27 14:10:55 [server] Peer Connection Initiated with [AF_INET]127.0.0.1:11194 2019-05-27 14:10:57 MANAGEMENT: >STATE:1558962657,GET_CONFIG,,,,,, 2019-05-27 14:10:57 SENT CONTROL [server]: 'PUSH_REQUEST' (status=1) 2019-05-27 14:10:57 PUSH: Received control message: 'PUSH_REPLY,redirect-gateway def1 bypass-dhcp,dhcp-option DNS 208.67.222.222,dhcp-option DNS 208.67.220.220,route 10.222.29.1,topology net30,ping 10,ping-restart 120,ifconfig 10.222.29.6 10.222.29.5,peer-id 0,cipher AES-256-GCM' 2019-05-27 14:10:57 OPTIONS IMPORT: timers and/or timeouts modified 2019-05-27 14:10:57 OPTIONS IMPORT: --ifconfig/up options modified 2019-05-27 14:10:57 OPTIONS IMPORT: route options modified 2019-05-27 14:10:57 OPTIONS IMPORT: --ip-win32 and/or --dhcp-option options modified 2019-05-27 14:10:57 OPTIONS IMPORT: peer-id set 2019-05-27 14:10:57 OPTIONS IMPORT: adjusting link_mtu to 1627 2019-05-27 14:10:57 OPTIONS IMPORT: data channel crypto options modified 2019-05-27 14:10:57 Data Channel: using negotiated cipher 'AES-256-GCM' 2019-05-27 14:10:57 Outgoing Data Channel: Cipher 'AES-256-GCM' initialized with 256 bit key 2019-05-27 14:10:57 Incoming Data Channel: Cipher 'AES-256-GCM' initialized with 256 bit key 2019-05-27 14:10:57 Opening utun (connect(AF_SYS_CONTROL)): Resource busy (errno=16) 2019-05-27 14:10:57 Opening utun (connect(AF_SYS_CONTROL)): Resource busy (errno=16) 2019-05-27 14:10:57 Opened utun device utun2 2019-05-27 14:10:57 do_ifconfig, tt->did_ifconfig_ipv6_setup=0 2019-05-27 14:10:57 MANAGEMENT: >STATE:1558962657,ASSIGN_IP,,10.222.29.6,,,, 2019-05-27 14:10:57 /sbin/ifconfig utun2 delete                                         ifconfig: ioctl (SIOCDIFADDR): Can't assign requested address 2019-05-27 14:10:57 NOTE: Tried to delete pre-existing tun/tap instance -- No Problem if failure 2019-05-27 14:10:57 /sbin/ifconfig utun2 10.222.29.6 10.222.29.5 mtu 1500 netmask 255.255.255.255 up 2019-05-27 14:10:57 /Applications/Tunnelblick.app/Contents/Resources/client.up.tunnelblick.sh -9 -d -f -m -w -ptADGNWradsgnw utun2 1500 1555 10.222.29.6 10.222.29.5 init                                         **********************************************                                         Start of output from client.up.tunnelblick.sh                                         Disabled IPv6 for 'iPhone USB'                                         Disabled IPv6 for 'Wi-Fi'                                         Disabled IPv6 for 'Bluetooth PAN'                                         Disabled IPv6 for 'Thunderbolt Bridge'                                         Retrieved from OpenVPN: name server(s) [ 208.67.222.222 208.67.220.220 ], search domain(s) [  ] and SMB server(s) [  ] and using default domain name [ openvpn ]                                         WARNING: Ignoring ServerAddresses '208.67.222.222 208.67.220.220' because ServerAddresses was set manually and '-allowChangesToManuallySetNetworkSettings' was not specified                                         Setting search domains to 'openvpn' because running under OS X 10.6 or higher and the search domains were not set manually (or are allowed to be changed) and 'Prepend domain name to search domains' was not selected                                         Saved the DNS and SMB configurations so they can be restored                                         Did not change DNS ServerAddresses setting of '1.1.1.1 1.0.0.1' (but re-set it)                                         Changed DNS SearchDomains setting from '' to 'openvpn'                                         Changed DNS DomainName setting from '' to 'openvpn'                                         Did not change SMB NetBIOSName setting of ''                                         Did not change SMB Workgroup setting of ''                                         Did not change SMB WINSAddresses setting of ''                                         DNS servers '1.1.1.1 1.0.0.1' were set manually                                         DNS servers '1.1.1.1 1.0.0.1' will be used for DNS queries when the VPN is active                                         NOTE: The DNS servers do not include any free public DNS servers known to Tunnelblick. This may cause DNS queries to fail or be intercepted or falsified even if they are directed through the VPN. Specify only known public DNS servers or DNS servers located on the VPN network to avoid such problems.                                         Flushed the DNS cache via dscacheutil                                         /usr/sbin/discoveryutil not present. Not flushing the DNS cache via discoveryutil                                         Notified mDNSResponder that the DNS cache was flushed                                         Setting up to monitor system configuration with process-network-changes                                         End of output from client.up.tunnelblick.sh                                         ********************************************** 2019-05-27 14:11:00 *Tunnelblick: No 'connected.sh' script to execute 2019-05-27 14:11:00 /sbin/route add -net 127.0.0.1 192.168.255.1 255.255.255.255                                         add net 127.0.0.1: gateway 192.168.255.1 2019-05-27 14:11:00 /sbin/route add -net 0.0.0.0 10.222.29.5 128.0.0.0                                         add net 0.0.0.0: gateway 10.222.29.5 2019-05-27 14:11:00 /sbin/route add -net 128.0.0.0 10.222.29.5 128.0.0.0                                         add net 128.0.0.0: gateway 10.222.29.5 2019-05-27 14:11:00 MANAGEMENT: >STATE:1558962660,ADD_ROUTES,,,,,, 2019-05-27 14:11:00 /sbin/route add -net 10.222.29.1 10.222.29.5 255.255.255.255                                         add net 10.222.29.1: gateway 10.222.29.5 2019-05-27 14:11:00 WARNING: this configuration may cache passwords in memory -- use the auth-nocache option to prevent this 2019-05-27 14:11:00 Initialization Sequence Completed 2019-05-27 14:11:00 MANAGEMENT: >STATE:1558962660,CONNECTED,SUCCESS,10.222.29.6,127.0.0.1,11194,127.0.0.1,55166 2019-05-27 14:11:24 Connection reset, restarting [-1] 2019-05-27 14:11:24 /sbin/route delete -net 10.222.29.1 10.222.29.5 255.255.255.255                                         delete net 10.222.29.1: gateway 10.222.29.5 2019-05-27 14:11:24 /sbin/route delete -net 127.0.0.1 192.168.255.1 255.255.255.255                                         delete net 127.0.0.1: gateway 192.168.255.1 2019-05-27 14:11:24 /sbin/route delete -net 0.0.0.0 10.222.29.5 128.0.0.0                                         delete net 0.0.0.0: gateway 10.222.29.5 2019-05-27 14:11:24 /sbin/route delete -net 128.0.0.0 10.222.29.5 128.0.0.0                                         delete net 128.0.0.0: gateway 10.222.29.5 2019-05-27 14:11:24 Closing TUN/TAP interface 2019-05-27 14:11:24 /Applications/Tunnelblick.app/Contents/Resources/client.down.tunnelblick.sh -9 -d -f -m -w -ptADGNWradsgnw utun2 1500 1555 10.222.29.6 10.222.29.5 init                                         **********************************************                                         Start of output from client.down.tunnelblick.sh                                         Cancelled monitoring of system configuration changes                                         Restored the DNS and SMB configurations                                         Re-enabled IPv6 (automatic) for 'iPhone USB'                                         Re-enabled IPv6 (automatic) for 'Wi-Fi'                                         Re-enabled IPv6 (automatic) for 'Bluetooth PAN'                                         Re-enabled IPv6 (automatic) for 'Thunderbolt Bridge'                                         Flushed the DNS cache via dscacheutil                                         /usr/sbin/discoveryutil not present. Not flushing the DNS cache via discoveryutil                                         Notified mDNSResponder that the DNS cache was flushed                                         End of output from client.down.tunnelblick.sh                                         ********************************************** 2019-05-27 14:11:25 SIGUSR1[soft,connection-reset] received, process restarting 2019-05-27 14:11:25 MANAGEMENT: >STATE:1558962685,RECONNECTING,connection-reset,,,,, 2019-05-27 14:11:25 *Tunnelblick: No 'reconnecting.sh' script to execute 2019-05-27 14:11:25 MANAGEMENT: CMD 'hold release' 2019-05-27 14:11:25 MANAGEMENT: CMD 'hold release' 2019-05-27 14:11:25 NOTE: the current --script-security setting may allow this configuration to call user-defined scripts 2019-05-27 14:11:25 Outgoing Control Channel Authentication: Using 160 bit message hash 'SHA1' for HMAC authentication 2019-05-27 14:11:25 Incoming Control Channel Authentication: Using 160 bit message hash 'SHA1' for HMAC authentication 2019-05-27 14:11:25 TCP/UDP: Preserving recently used remote address: [AF_INET]127.0.0.1:11194 2019-05-27 14:11:25 Socket Buffers: R=[131072->131072] S=[131072->131072] 2019-05-27 14:11:25 Attempting to establish TCP connection with [AF_INET]127.0.0.1:11194 [nonblock] 2019-05-27 14:11:25 MANAGEMENT: >STATE:1558962685,TCP_CONNECT,,,,,, 2019-05-27 14:11:26 TCP connection established with [AF_INET]127.0.0.1:11194 2019-05-27 14:11:26 TCP_CLIENT link local: (not bound) 2019-05-27 14:11:26 TCP_CLIENT link remote: [AF_INET]127.0.0.1:11194 2019-05-27 14:11:26 MANAGEMENT: >STATE:1558962686,WAIT,,,,,, 2019-05-27 14:11:26 MANAGEMENT: >STATE:1558962686,AUTH,,,,,, 2019-05-27 14:11:26 TLS: Initial packet from [AF_INET]127.0.0.1:11194, sid=072914d3 4912c8a0 2019-05-27 14:11:26 VERIFY OK: depth=1, C=US, ST=CA, L=San Francisco, O=TurnKey Linux, OU=OpenVPN, CN=server, name=openvpn, emailAddress=vpn@radged.com 2019-05-27 14:11:26 VERIFY KU OK 2019-05-27 14:11:26 Validating certificate extended key usage 2019-05-27 14:11:26 ++ Certificate has EKU (str) TLS Web Server Authentication, expects TLS Web Server Authentication 2019-05-27 14:11:26 VERIFY EKU OK 2019-05-27 14:11:26 VERIFY OK: depth=0, C=US, ST=CA, L=San Francisco, O=TurnKey Linux, OU=OpenVPN, CN=server, name=openvpn, emailAddress=vpn@radged.com 2019-05-27 14:11:26 WARNING: 'link-mtu' is used inconsistently, local='link-mtu 1552', remote='link-mtu 1544' 2019-05-27 14:11:26 WARNING: 'cipher' is used inconsistently, local='cipher AES-256-GCM', remote='cipher BF-CBC' 2019-05-27 14:11:26 WARNING: 'auth' is used inconsistently, local='auth [null-digest]', remote='auth SHA1' 2019-05-27 14:11:26 WARNING: 'keysize' is used inconsistently, local='keysize 256', remote='keysize 128' 2019-05-27 14:11:26 Control Channel: TLSv1.2, cipher TLSv1/SSLv3 ECDHE-RSA-AES256-GCM-SHA384, 2048 bit RSA 2019-05-27 14:11:26 [server] Peer Connection Initiated with [AF_INET]127.0.0.1:11194 2019-05-27 14:11:26 *Tunnelblick: Disconnecting; notification window disconnect button pressed 2019-05-27 14:11:27 *Tunnelblick: No 'pre-disconnect.sh' script to execute 2019-05-27 14:11:27 *Tunnelblick: Disconnecting using 'kill' 2019-05-27 14:11:27 event_wait : Interrupted system call (code=4) 2019-05-27 14:11:27 SIGTERM[hard,] received, process exiting 2019-05-27 14:11:27 MANAGEMENT: >STATE:1558962687,EXITING,SIGTERM,,,,, 2019-05-27 14:11:27 *Tunnelblick: No 'post-disconnect.sh' script to execute 2019-05-27 14:11:27 *Tunnelblick: Expected disconnection occurred. 

Cloudfront with Nginx 302 redirect – resolve internally

Currently, We have hosted our application on two different paths, App1: https://website.wordpress.com [EC2 with Nginx] App2: https://poc.angularApp.com/ [Hosted in AWS S3 with Coludfront]

My Requirements are:

Whenever user client login then it should rewrite to app2 location without changing the URL, Ex,

App1: https://website.wordpress.com/member App2: https://poc.angularApp.com/member

Here is my current Nginx conf,

location /member { proxy_pass https://poc.angularApp.com;
proxy_intercept_errors on; error_page 301 302 307 = @handle_redirects; }

location @handle_redirects {     set $  saved_redirect_location '$  upstream_http_location';     proxy_pass $  saved_redirect_location; } 

Any solution please?

SharePoint 2016 Internally Hosted w/ External Users

This question is about an internally hosted SharePoint 2016 server. Information about how to do this with the SharePoint Cloud/SAAS is abundant and clear.

I would like to set up an internally hosted SharePoint 2016 server and allow users external to my domain (i.e. clients) to access sites on that server. I understand how to do the networking stuff. My question is about how to set up accounts with SharePoint that are for users that are not members of the domain SharePoint leverages.

The number of external users I allow access will be small per client, only one or two. Setting up a trust relationship or whatever between our organizations won’t work.

Boiled down to as simple as I can get it, I want to tell SharePoint to grant access on “Site 1” to “the_product_owner@my_client.com”. Or whatever the path is, preferably without giving that user an account on my network / domain.

I’ve burned quite a bit of time with various permutations of search terms to figure this out, and all I’ve uncovered so far is that it’s super simple with SharePoint on the cloud and potentially impossible with SharePoint self-hosted.

Am I attempting the impossible? If not, could you please point me to information that describes how to do it?

Thank you!

If $S, S_1, S_2$ be the circles of radii 5,3 and 2 respectively. If $S_1$ and $S_2$ touch externally and they touch internally with $S$.

If $ S, S_1, S_2$ be the circles of radii 5,3 and 2 respectively. If $ S_1$ and $ S_2$ touch externally and they touch internally with $ S$ . The radius of circle $ S_3$ which touches externally with $ S_1$ and $ S_2$ and internally with $ S$ is?

I tried making a diagram and figuring out, but cannot bring a relation.